satellite communication

EURASIP Journal on Wireless Communications and Networking

Satellite Communications

Guest Editors: Ray E. Sheriff, Anton Donner, and Alessandro Vanelli-Coralli

EURASIP Journal onWireless Communications and Networking


Guest Editors: Ray E. Sheriff, Anton Donner,and Alessandro Vanelli-Coralli

Copyright © 2007 Hindawi Publishing Corporation. All rights reserved.

This is a special issue published in volume 2007 of “EURASIP Journal on Wireless Communications and Networking.” All articles areopen access articles distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, andreproduction in any medium, provided the original work is properly cited.

Editor-in-ChiefLuc Vandendorpe, Universite Catholique de Louvain, Belgium

Associate EditorsThushara Abhayapala, AustraliaMohamed H. Ahmed, CanadaFarid Ahmed, USAAlagan Anpalagan, CanadaAnthony Boucouvalas, GreeceLin Cai, CanadaBiao Chen, USAYuh-Shyan Chen, TaiwanPascal Chevalier, FranceChia-Chin Chong, South KoreaHuaiyu Dai, USASoura Dasgupta, USAIbrahim Develi, TurkeyPetar M. Djuric, USAMischa Dohler, FranceAbraham O. Fapojuwo, CanadaMichael Gastpar, USAAlex Gershman, GermanyWolfgang Gerstacker, Germany

David Gesbert, FranceFary Z. Ghassemlooy, UKChristian Hartmann, GermanyStefan Kaiser, GermanyG. K. Karagiannidis, GreeceChi Chung Ko, SingaporeVisa Koivunen, FinlandRichard Kozick, USABhaskar Krishnamachari, USAS. Lambotharan, UKVincent Lau, Hong KongDavid I. Laurenson, UKTho Le-Ngoc, CanadaWei Li, USAYonghui Li, AustraliaTongtong Li, USAZhiqiang Liu, USAStephen McLaughlin, ScotlandSudip Misra, Canada

Marc Moonen, BelgiumEric Moulines, FranceSayandev Mukherjee, USAKameswara Rao Namuduri, USAAmiya Nayak, CanadaA. Pandharipande, The NetherlandsAthina Petropulu, USAA. Lee Swindlehurst, USASergios Theodoridis, GreeceGeorge S. Tombras, GreeceLang Tong, USAAthanasios V. Vasilakos, GreeceWeidong Xiang, USAYang Xiao, USAXueshi Yang, USALawrence Yeung, Hong KongDongmei Zhao, CanadaWeihua Zhuang, Canada

Contents

Satellite Communications, Ray E. Sheriff, Anton Donner, and Alessandro Vanelli-CoralliVolume 2007, Article ID 58964, 2 pages

Multi-Satellite MIMO Communications at Ku-Band and Above: Investigations on Spatial Multiplexingfor Capacity Improvement and Selection Diversity for Interference Mitigation, Konstantinos P. Liolis,Athanasios D. Panagopoulos, and Panayotis G. CottisVolume 2007, Article ID 59608, 11 pages

Investigations in Satellite MIMO Channel Modeling: Accent on Polarization, Peter Horvath,George K. Karagiannidis, Peter R. King, Stavros Stavrou, and Istvan FrigyesVolume 2007, Article ID 98942, 10 pages

Performance Analysis of SSC Diversity Receivers over Correlated Ricean Fading Satellite Channels,Petros S. Bithas and P. Takis MathiopoulosVolume 2007, Article ID 25361, 9 pages

Advanced Fade Countermeasures for DVB-S2 Systems in Railway Scenarios, Stefano Cioni,Cristina Parraga Niebla, Gonzalo Seco Granados, Sandro Scalise, Alessandro Vanelli-Coralli,and Marıa Angeles Vazquez CastroVolume 2007, Article ID 49718, 17 pages

Capacity Versus Bit Error Rate Trade-Off in the DVB-S2 Forward Link, Matteo Berioli,Christian Kissling, and Remi LapeyreVolume 2007, Article ID 14798, 10 pages

Frequency Estimation in Iterative Interference Cancellation Applied to Multibeam Satellite Systems,J. P. Millerioux, M. L. Boucheret, C. Bazile, and A. DucasseVolume 2007, Article ID 62310, 12 pages

A QoS Architecture for DVB-RCS Next Generation Satellite Networks, Thierry Gayraud andPascal BerthouVolume 2007, Article ID 58484, 9 pages

Maximum Likelihood Timing and Carrier Synchronization in Burst-Mode Satellite Transmissions,Michele Morelli and Antonio A. D’AmicoVolume 2007, Article ID 65058, 8 pages

Burst Format Design for Optimum Joint Estimation of Doppler-Shift and Doppler-Rate in PacketSatellite Communications, Luca Giugno, Francesca Zanier, and Marco LuiseVolume 2007, Article ID 29086, 12 pages

TCP-Call Admission Control Interaction in Multiplatform Space Architectures, Georgios Theodoridis,Cesare Roseti, Niovi Pavlidou, and Michele LuglioVolume 2007, Article ID 23923, 8 pages

Efficient Delay Tracking Methods with Sidelobes Cancellation for BOC-Modulated Signals,Adina Burian, Elena Simona Lohan, and Markku Kalevi RenforsVolume 2007, Article ID 72626, 20 pages

Analysis of Filter-Bank-Based Methods for Fast Serial Acquisition of BOC-Modulated Signals,Elena Simona LohanVolume 2007, Article ID 25178, 12 pages

Hindawi Publishing CorporationEURASIP Journal on Wireless Communications and NetworkingVolume 2007, Article ID 58964, 2 pagesdoi:10.1155/2007/58964

EditorialSatellite Communications

Ray E. Sheriff,1 Anton Donner,2 and Alessandro Vanelli-Coralli3

1 Mobile and Satellite Communications Research Centre, School of Engineering, Design and Technology, University of Bradford,Richmond Road Bradford BD7 1DP, UK

2 German Aerospace Center, Institute of Communications and Navigation, Oberpfaffenhofen, 82234 Wessling, Germany3 ARCES, University of Bologna, Via Toffano 2, 40125 Bologna, Italy

Received 28 November 2007; Accepted 9 December 2007

Copyright © 2007 Ray E. Sheriff et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

We are delighted to bring to you this special issue on satel-lite communications, which we have prepared as part of thespreading of excellence remit of the satellite communica-tions network of excellence (SatNEx). The SatNEx project,which began in 2004, is funded for five years under the Euro-pean Union’s Sixth Framework Programme (FP6) Informa-tion Society Technologies (IST) Thematic Area. Led by theGerman Aerospace Center, SatNEx brings together a networkof 24 partners, distributed throughout Europe, with mem-bership drawn from ten countries.

The philosophy underlying the SatNEx approach re-volves around the selection of focused actions under JointProgrammes of Activities, which are carried out collectivelyby the partners and include research, integration, and dis-semination activities. Training represents an important partof the SatNEx remit and is supported through a number ofinitiatives including the hosting of internship projects and anannual summer school.

The call for papers resulted in a high number of submis-sions, from which we have been able to select 12 excellentpapers dealing with the different aspects of satellite commu-nications and navigation.

Multiple-input multiple-output (MIMO) techniques areattracting a considerable amount of attention from withinthe terrestrial wireless community. The first paper of this spe-cial issue, “Multisatellite MIMO communications at Ku bandand above: investigations on spatial multiplexing for capac-ity improvement and selection diversity for interference mit-igation,” considers the application of such technology over asatellite platform operating in the Ku band and above. Thepaper considers how MIMO can be used to increase capac-ity by using a satellite spatial multiplexing system and howantenna selection can be used to mitigate interference. Thenext paper “Investigations in satellite MIMO channel model-

ing: accent on polarization” looks at MIMO systems from thepolarization diversity point of view and dwells on the satellitecooperative communication concepts.

Switch and stay combining (SSC) is a form of diversitytechnique used in digital receivers to compensate for fadeevents introduced by the mobile channel. The third paper“Performance analysis of SSC diversity receivers over corre-lated Ricean fading satellite channels” investigates the per-formance of dual-branch SSC receivers for different fadingchannel characteristics.

The next four papers deal with the emerging scenarioof mobile digital video broadcasting (DVB-S2 and RCS mo-bile). Alternative approaches to counteracting fading chan-nels introduced when operating in a train environment re-ceiving satellite DVB-S2 are presented in the paper “Ad-vanced fade countermeasures for DVB-S2 systems in railwayscenarios.” Here, as a result of simulation analysis, antennadiversity and packet-level forward error correction mecha-nisms are proposed and their impact is evaluated with respectto the receiver design and system complexity. The theme ofDVB-S2 is continued with the paper “Capacity versus bit er-ror rate trade-off in the DVB-S2 forward link,” which inves-tigates how satellite capacity can be optimised for DVB-S2transmissions. The DVB return channel via satellite (DVB-RCS) is then addressed in “Frequency estimation in iterativeinterference cancellation applied to multibeam satellite sys-tems,” which considers the application of interference cancel-lation on the reverse link of a multibeam satellite system, us-ing DVB-RCS with convolutional coding as an example. Thepaper “A QoS architecture for DVB-RCS next-generationsatellite networks” proceeds to design and emulate a quality-of-service (QoS) architecture that demonstrates using realmultimedia applications how QoS can be supported over aDVB-RCS network.

2 EURASIP Journal on Wireless Communications and Networking

Synchronization aspects are dealt with in “Maximumlikelihood timing and carrier synchronization in burst-modesatellite transmissions.” The paper addresses the problem ofachieving synchronisation for a burst-mode satellite trans-mission over an AWGN channel. The subject of burst trans-mission continues with the paper “Burst format design foroptimum joint estimation of Doppler-shift and Doppler-rate in packet satellite communications,” which considersoptimising the burst-format of packet-oriented transmis-sions by proposing very-low-complexity algorithms for car-rier Doppler-shift and Doppler-rate estimation.

A network comprising satellite and high-altitude plat-forms is considered in the paper “TCP-call admission con-trol interaction in multiplatform space architectures.” Cross-layer techniques are implemented by means of TCP feedingback into call admission control (CAC) procedures for thepurpose of prevention of congestion and improvement inQoS.

Finally, since navigation is an extremely important partof the satellite system family, we have included two papers.The first paper “Efficient delay tracking methods with side-lobes cancellation for BOC-modulated signals” deals with bi-nary offset carrier (BOC) modulation, which is adopted intypical navigation systems. The paper considers how to im-prove the tracking of the main lobe of the BOC-modulatedsignal by using sidelobe suppression techniques. An alterna-tive approach based on filter bank processing is presented in“Analysis of filter-bank-based methods for fast serial acqui-sition of BOC-modulated signals” to conclude the special is-sue.

ACKNOWLEDGMENTS

It has been a pleasure for us to have put together this spe-cial issue, which we hope you will find interesting. We wouldlike to thank the editorial staff at Hindawi for their sup-port and assistance during the preparation of this special is-sue. We would like to thank the contributing authors for theexcellent quality of their submissions and our SatNEx col-leagues for their valuable assistance in the reviewing of pa-pers. SatNEx is partially funded by the European Commis-sion under the Sixth Framework Programme. Further in-formation on SatNEx can be found on the project web site:http://www.satnex.org/.

Ray E. SheriffAnton Donner

Alessandro Vanelli-Coralli


Research ArticleMulti-Satellite MIMO Communications at Ku-Band andAbove: Investigations on Spatial Multiplexing for CapacityImprovement and Selection Diversity forInterference Mitigation

Konstantinos P. Liolis, Athanasios D. Panagopoulos, and Panayotis G. Cottis

Wireless & Satellite Communications Group, School of Electrical and Computer Engineering, National Technical University of Athens(NTUA), 9 Iroon Polytechniou Street, Zografou, Athens 15780, Greece

Received 28 August 2006; Revised 2 March 2007; Accepted 13 May 2007

Recommended by Alessandro Vanelli-Coralli

This paper investigates the applicability of multiple-input multiple-output (MIMO) technology to satellite communications at theKu-band and above. After introducing the possible diversity sources to form a MIMO matrix channel in a satellite environment,particular emphasis is put on satellite diversity. Two specific different topics from the field of MIMO technology applications tosatellite communications at these frequencies are further analyzed: (i) capacity improvement achieved by MIMO spatial multi-plexing systems and (ii) interference mitigation achieved by MIMO diversity systems employing receive antenna selection. In thefirst case, a single-user capacity analysis of a satellite 2× 2 MIMO spatial multiplexing system is presented and a useful analyticalclosed form expression is derived for the outage capacity achieved. In the second case, a satellite 2×2 MIMO diversity system withreceive antenna selection is considered, adjacent satellite cochannel interference on its forward link is studied and an analyticalmodel predicting the interference mitigation achieved is presented. In both cases, an appropriate physical MIMO channel model isassumed which takes into account the propagation phenomena related to the frequencies of interest, such as clear line-of-sight op-eration, high antenna directivity, the effect of rain fading, and the slant path lengths difference. Useful numerical results obtainedthrough the analytical expressions derived are presented to compare the performance of multi-satellite MIMO systems to relevantsingle-input single-output (SISO) ones.

Copyright © 2007 Konstantinos P. Liolis et al. This is an open access article distributed under the Creative Commons AttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properlycited.

1. INTRODUCTION

Multiple-input multiple-output (MIMO) technology has re-cently emerged as one of the most significant technicalbreakthroughs in modern digital communications due to itspromise of very high data rates at no cost of extra spectrumand transmit power [1, 2]. Wireless communication can bebenefited from MIMO signaling in two different ways: spa-tial multiplexing and diversity. In the former case, indepen-dent data is transmitted from separate antennas, and aimingat maximizing throughput (i.e., linear capacity growth withthe number of antennas can be achieved). In the latter case,the same signal is transmitted along multiple (ideally) inde-pendently fading paths aiming at improving the robustnessof the link in terms of each user BER performance. Theseadvantages have been largely responsible for the success of

MIMO both as a research topic and as a commercially viabletechnology in terrestrial communications [1, 2].

The appealing gains obtained by MIMO techniques interrestrial networks generate a further interest in investigat-ing the possibility of applying the same principle in satel-lite networks, as well. However, the underlying differencesbetween the terrestrial and the satellite channels make suchapplicability a non straightforward matter and, therefore, arather challenging subject. In this case, one of the funda-mental problems is the difficulty of generating a completelyindependent fading profile over the space segment. In satel-lite communications, due to the huge free space losses alongthe earth-space link, line-of-sight (LOS) operation is usuallydeemed a practical necessity. However, this is not the typ-ical case in terrestrial communications where rich scatter-ing and non-LOS environments with multipath propagation


are encountered. Thus, placing multiple antennas on a sin-gle satellite does not seem a suitable choice in order to ex-ploit the MIMO channel capabilities. In fact, the absence ofscatterers in the vicinity of the satellite leads to an inherentrank deficiency of the MIMO channel matrix. Therefore, at afirst glance, the applicability of MIMO technology to satellitechannels does not seem well justified.

The objective of this paper is in line with some other re-cent research efforts [4–8, 12–16] casting further light in thisregard. These studies have been mainly concerned with thepossible diversity sources that can be exploited in satellitecommunications to form a MIMO matrix channel. A cate-gorization of these diversity sources follows.

(i) Site diversity, where multiple cooperating terminalstations (TSs), sufficiently separated from each other, are incommunication with a single satellite. So far, it has only beenstudied as an efficient rain fade mitigation technique at theKu (12/14 GHz), Ka (20/30 GHz), and Q/V (40/50 GHz) fre-quency bands because of its very low achievable spatial cor-relation due to rain [3]. However, due to the enormous slantpath lengths associated, the required separation distance be-tween the multiple TSs to ensure ideally independent fadingprofile is of the order of several km, which rather hinders itspractical interest in MIMO applications.

(ii) Satellite (or orbital) diversity, where multiple satel-lites, sufficiently separated in orbit to provide (ideally) in-dependently fading channels, communicate with a single TSequipped with either multiple antennas or even a single mul-tiple-input antenna. So far, it has been studied mostly as anefficient rain fade mitigation technique in Ku-, Ka-, and Q/V-band satellite communications [3] and, also, recently, as acandidate to form satellite MIMO matrix channels at high(i.e., Ku, Ka, and Q/V) [4, 5] as well as at low frequencybands, such as L (1/2 GHz) and S (2/4 GHz) [6–8]. Also, itis worthwhile noting that it is already successfully employedin the continental US digital audio radio services (DARS),mobile systems, Sirius and XM satellite radio, operating atthe S-band [9]. Satellite diversity provides a rather practicalsolution of reasonable complexity since the multiple receivedsignals at the single TS can easily be combined due to thecolocation of the antennas. However, an inherent problemof this scheme, apart from the costly utilization of multiplesatellites, is the asynchronism of the multiple transmitted sig-nals at the TS receiver, which comes as a result of the prop-agation delay difference due to the wide separation betweenthe satellites. A similar problem is dealt with and solutionsare proposed in several papers mainly concerning distributedsensor networks, such as in [10]. To the authors’ knowledge,for the more complicated satellite case—due to the muchlarger and variable delay difference—the only relevant solu-tion proposed so far is reported in [5].

(iii) Polarization diversity, where a single dual-orthogonalpolarized satellite communicates with a single TS equippedwith a dual-orthogonal polarized antenna. Its principle isbased on the polarization sensitivity of the reflection anddiffraction processes, which causes random signal fading atthe TS receiver. It represents a solution of rather practicalinterest due to the recent developments in MIMO compact

antennas (see, e.g., [11]) which allow for compact MIMOsetups. It has already been examined as a promising solu-tion to shape MIMO channels in S-band land mobile satellitecommunications [7, 12–16]. Its main advantage over satellitediversity is the elimination of any additional cost associatedwith the utilization of multiple satellites. It also bypasses theasynchronism problem associated with the distributed na-ture of satellite diversity. However, it can be disadvantageousto satellite diversity especially in satellite networks operatingat high-frequency bands (i.e., Ku, Ka, and Q/V), which areaffected by the highly correlated rainfall medium and, also,in case of large blockages resulting in hard system failures(i.e., on/off channel phenomena). Moreover, as concluded in[13], polarization diversity can only increase the transmis-sion rate of a satellite communication system by a factor oftwo, whereas in multi-satellite systems, satellite diversity canresult in m-fold capacity increase, where m is the number ofsatellites occupied.

This paper focuses particularly on dual-satellite MIMOcommunication systems employing satellite diversity. More-over, emphasis is put on the less congested high-frequencybands, such as Ku and above. At these frequencies, multi-path propagation is insignificant. However, by virtue of satel-lite diversity, MIMO can be considered to effectively exploitthe rainfall spatial inhomogeneity instead. A physical 2 × 2MIMO satellite channel model is assumed taking into ac-count the relevant propagation phenomena, such as clearLOS operation, high antenna directivity, rain fading, andrainfall spatial inhomogeneity [3, 17]. This model is flexi-ble and can be applied on a global scale since it has physicalinputs obtained by regression fitting analysis on the ITU-Rrainmaps [18] and is based on general assumptions aboutthe rain process [17]. Moreover, it incorporates the generalcase of an ordered MIMO satellite channel (due to the slantpath lengths difference). To this end, the resulting propaga-tion delay offset is assumed to be properly taken into accountat the TS receiver. A possible practical solution to this prob-lem might be the one implemented in [5] according to whichmatched filters are first applied to the received signals for thedetection of the propagation delay offset, which is then fed toa timing aligner. Subsequently, the proposed timing alignereliminates the delay offset by adjusting the timing of a signalparallel-to-serial converter. The study of more efficient solu-tions to the asynchronism problem associated with satellitediversity, although rather challenging, is out of the scope ofthis paper and will be the subject of a future work.

In the first part of this work, emphasis is put on a satellite2 × 2 MIMO spatial multiplexing system and on its possi-ble capacity improvement with respect to the relevant SISOsystem. The term “spatial multiplexing” refers to the trans-mission of independent data streams from the multiple sep-arate satellites [1, 2]. Well-known results obtained from theMIMO literature [19, 20] are applied here for the capacityanalysis of such a 2 × 2 MIMO system. The figure of meritused to characterize the resulting MIMO fading channel isthe outage capacity [1], for which an analytical closed formexpression is provided. Note that such analytical expressionsare extremely hard to obtain even in the well-established field

Konstantinos P. Liolis et al. 3

S1 S2

d1,AR1 d2,AR2

Δθ

TS

(a)

To S1To S2

ϕ2ϕ1

TS

(b)

Figure 1: (a) Configuration of a dual-satellite 2× 2 MIMO channel. Individual satellites S1 and S2 transmit either independent data streams(MIMO spatial multiplexing system, Section 3) or the same signal over the multiple (ideally) independently fading paths (MIMO diversitysystem, Section 4), (b) associated elevation angles.

of MIMO theory due to the intractability of the outage ca-pacity distribution [2].

In the second part, a satellite 2 × 2 MIMO diversity sys-tem employing receive antenna selection is examined, andissues specifically related to cochannel interference (CCI) areaddressed from a propagation point of view. The term “di-versity” refers to the transmission of the same signal over themultiple (ideally) independently fading paths [1, 2]. Receiveantenna selection is a low-cost, low-complexity approach tobenefit from many of the advantages of MIMO technologywhile, at the same time, bypassing the multiple RF chainsassociated with multiple antennas at the receiver, which arecostly in terms of size, power, and hardware [21]. The inter-ference analysis presented here is quite different from con-ventional communication-oriented approaches followed instandard MIMO theory [1]. Attention is paid to the CCIproblems arising on the forward link of such a 2 × 2 MIMOsatellite system due to differential rain attenuation from anadjacent satellite [22]. To deal with the statistical behaviourof the signal-to-interference ratio (SIR) introduced by therainfall spatial inhomogeneity, the concept of unacceptableinterference probability1 [23, 24] is employed here. An ana-lytical prediction model concerning the interference mitiga-tion achieved by the proposed satellite 2× 2 MIMO diversitysystem is provided.

The rest of the paper is organized as follows. Section 2presents the channel model adopted for MIMO satellite com-munications at the Ku-band and above. Section 3 provides acommunication-based capacity analysis for a satellite 2 × 2MIMO spatial multiplexing system. A propagation-oriented

1 Note that the concept of the “unacceptable interference probability(UIP)” in this paper is exactly the same as that of the “acceptable interfer-ence probability (AIP)” employed in [23, 24]. Their only difference con-cerns their nomenclature.

analysis for the possible interference mitigation achieved by asatellite 2×2 MIMO diversity system with receive antenna se-lection is presented in Section 4. Useful numerical results ob-tained for both the above satellite MIMO applications con-sidered are provided in Section 5. Section 6 concludes thepaper.

2. MIMO SATELLITE CHANNEL MODEL

Figure 1 depicts the configuration of a dual-satellite MIMOcommunication channel at the Ku-band and above. The TSis equipped with two colocated highly directive antennas andcommunicates with two satellites, S1 and S2, subtending anangle Δθ to the TS, large enough that the spatial correlationdue to rain along the relevant slant paths is as low as possible.The normalized radiation pattern of each TS antenna, de-noted by GR(·), is compatible with the ITU-R specifications[25] and is shown in Figure 2.2 The lengths of slant pathsSi-TS are denoted by di (i = 1, 2) and the random variables(RVs) associated with the respective rain induced attenua-tions (in dB) are denoted by ARi (i = 1, 2). In general, thetwo slant paths Si-TS have different elevation angles denotedby φi (i = 1, 2), respectively.

Assuming that clear LOS between the TS and each satel-lite Si exists, that each TS antenna is at boresight with thecorresponding satellite Si (i = 1, 2) and that rain attenuationis the major fading mechanism, the path gain for each Si-TSlink is modeled as

gi ∝ GR(0◦) · d−2

i · 10−ARi/10 (i = 1, 2). (1)

2 Note that the analyses presented hereafter are quite general and, therefore,may incorporate other TS antenna radiation patterns, as well.


−100 −80 −60 −40 −20 0 20 40 60 80 100

Off-axis angle (deg)

−40

−35

−30

−25

−20

−15

−10

−5

0

TS

ante

nn

an

orm

aliz

edga

in,G

R(d

B)

Figure 2: Normalized radiation pattern of each TS antenna com-patible with ITU-R specifications [25].

Hence, the total path loss along each Si-TS link (in dB) is

Ai = FSLi + ARi (i = 1, 2), (2)

where FSLi = 10 log10(4πdi f /c)2 is the free space loss alongeach link, c the speed of light, and f the operating fre-quency. Note that the fundamental assumptions concerningthe modeling of the rain attenuation RVs ARi (i = 1, 2) arethe same as those analytically presented in [17]. The convec-tive raincell model employing Crane’s assumptions is usedfor the description of the vertical variation of the rainfallstructure [17]. Based on this assumption, if Δθ is sufficientlylarge, the spatial correlation coefficient between the RVs ARiis relatively low and, thus, an (ideally) decorrelated MIMOsatellite channel is possible. To this end, an illustrative quan-titative example is presented in Figure 3, which depicts thespatial correlation coefficient due to rain ρ12 versus Δθ for adual-satellite MIMO channel operating in Atlanta, GA, USAat the Ka-band with satellite elevation angles φ1 = 45◦ andφ2 = 40◦.

Based on the above and, also, assuming frequency nonse-lective fading, the resulting MIMO channel matrix H is givenby

H =[h11 h12

h21 h22

]

=

⎡

⎢⎢⎣

√g1 exp

(j2πd1 f

c

)0

0 √g2 exp

(j2πd2 f

c

)

⎤

⎥⎥⎦ .

(3)

The diagonal structure of H is due to the high directivity ofthe TS antennas and the large value of Δθ. In MIMO ter-minology, channels with diagonal H matrix are known asparallel MIMO channels. Further details about such chan-nels can be found in [26]. Moreover, as opposed to standardMIMO theory [1, 2], H is not normalized here (i.e., orderedMIMO channel) due to the different slant path lengths di

0 20 40 60 80 100 120 140 160 180

Angular separation, Δθ (deg)

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Spat

ialc

orre

lati

onco

effici

ent

due

tora

in,ρ

12

Figure 3: Spatial correlation coefficient due to rain ρ12 versus an-gular separation Δθ for a dual-satellite MIMO channel operating inAtlanta, GA, at the Ka-band with satellite elevation angles φ1 = 45◦

and φ2 = 40◦.

(i = 1, 2). Finally, the assumption of independent identicallydistributed (i.i.d) elements of H, often made in conventionalterrestrial MIMO systems, cannot be made here, since thereis a relatively high spatial correlation due to rain.

3. SATELLITE MIMO SPATIAL MULTIPLEXING SYSTEM:CAPACITY ANALYSIS

In this Section, the two satellites Si (i = 1, 2) depicted inFigure 1 are assumed to transmit different and independentdata streams (i.e., spatial multiplexing is investigated). Thechannel H is considered perfectly known to the TS receiver(via training and tracking), while at the transmit side, bothsatellites are assumed to have no channel knowledge. In theabsence of channel state information (CSI) at the transmitside, equal power allocation to the two satellites is a reason-able and rather practical choice, due to the distributed na-ture of the system. Therefore, from the standard MIMO the-ory, the following well-known formula for the capacity (inbps/Hz) of MIMO channels is adopted [19, 20]:

C = log2 det(

I2 +PT

2N0HHH

)=

2∑

i=1

log2

(1 +

PT2N0

λi

),

(4)

where I2 is the 2 × 2 identity matrix, PT the total averagepower available at the transmit side,3 N0 the noise spectral

3 Note that PT is the sum transmit power of all transmitting satellites Si re-gardless of their number. This means that in both the dual-satellite MIMOcase and the single satellite SISO case, the total available transmit poweris constant and equal to PT . This is ensured employing the normalizationfactor “2” in (4), which allows for a fair comparison between the relevantMIMO and SISO cases.


density at the TS receiver input, and λi (i = 1, 2) the positiveeigenvalues of the matrix HHH (the superscript H stands forconjugate transposition).

Taking into account the channel modeling assumptions,(4) is written as

C =2∑

i=1

log2

(1 + 0.5SNRCSi10−ARi/10), (5)

where SNRCSi (i = 1, 2) are the nominal SNR values underclear sky conditions. Based on the path gain model given in(1), the SNRCSi values (in dB) are related through

SNRCS1 − SNRCS2 = 20 log10

(d2

d1

). (6)

Equation (5) provides an expression for the instantaneouscapacity of a deterministic 2 × 2 MIMO channel H. How-ever, since the rainfall introduces slow fading and stochasticbehaviour over the channel H, the appropriate statistic mea-sure to characterize the resulting fading channel is the outagecapacity defined by [1]

P(C ≤ Cout,q

) = q, (7)

where Cout,q is the information rate guaranteed for (1−q)100% of the channel realizations.

Consider the RV transformation

ui =[

ln(ARi

)− ln(AmRi

)]

SaRi(i = 1, 2) (8)

which relates the lognormal rain attenuation RVs ARi (i =1, 2) to the normalized normal RVs ui (i = 1, 2). Substituting(5) into (7) and after some straightforward algebra, the fol-lowing analytical closed form expression for the outage ca-pacity is obtained:

P(C ≤ Cout,q

)

= 12

∫ +∞

uAdu1 fU1

(u1)

erfc

(uB − ρn12u1√2(1− ρ2

n12

)

)

= q,

(9)

where erfc(·) is the complementary error function, fU1 (u1)the probability density function (pdf) of the normal distri-bution, ρn12 the logarithmic correlation coefficient betweenthe normal RVs ui (i = 1, 2) [17] and uA, uB are analyticallygiven by

uA =[

ln(10 log10

(0.5SNRCS2

)− 10 log10

(2Cout,q − 1

))

− ln(AmR2

)]/SaR2 ,

(10)

uB =[

ln(10 log10

(0.5SNRCS1

)

+ 10 log10

(1 + 0.5SNRCS210−AmR2 exp(u1SaR2 )/10)

−10 log10

(2Cout,q−1−0.5SNRCS210−AmR2 exp(u1SaR2 )/10))

− ln(AmR1

)]/SaR1 .

(11)

The quantities AmRi , SaRi (i = 1, 2), encountered in (8)–(11),are the statistical parameters of the lognormal RVs ARi (i =1, 2) given by [17]

S2aRi = ln

[1 +

Hi

L2Di

(exp

(b2S2

r

)− 1)]

(i = 1, 2),

AmRi = aRbmLDi exp(b2S2

r − S2aRi

2

)(i = 1, 2),

(12)

where LDi (i = 1, 2) are the projections of the effective pathlengths Li (i = 1, 2) [17] on the earth surface, Hi (i = 1, 2) arespatial parameters related to each path of length LDi (i = 1, 2)which may be found in [17], and a, b are constants depend-ing on the operating frequency f , the polarization tilt angle,the temperature, and the rainfall characteristics over the ser-viced area. Rm, Sr are the lognormal statistical parameters ofthe rainfall rate R (in mm/hr). A reliable database of rainfallstatistics for any geographical location on earth is providedby ITU-R in [18] and is used throughout the present work asan input to the simulations performed in order to determinethe values of Rm, Sr .

4. SATELLITE MIMO DIVERSITY SYSTEMWITH RECEIVE ANTENNA SELECTION:INTERFERENCE ANALYSIS

In this section, the two satellites Si (i = 1, 2) depicted inFigure 1 are assumed to transmit the same signal over the(ideally) independently fading paths Si-TS (i = 1, 2) (i.e., di-versity is investigated). To alleviate the high cost and com-plexity associated with multiple RF chains, the dual-antennaTS receiver is equipped with only one RF chain and performsantenna selection, that is, the 2 × 2 MIMO satellite systemassumed employs receive selection diversity [21]. Therefore,the TS receiver detects the signal related to the path with thehighest SNR. Under the constraint of only one RF chain atthe receiver, in order to know all SNRs simultaneously foroptimal selection, a training signal in a preamble to the trans-mitted data is assumed. During this preamble, the TS receiverscans the two antennas, finds that one with the highest SNR,and selects it for reception of the next data burst. Thus, onlya few more training bits are required instead of additional RFchains.

Particular emphasis is put on possible interference mit-igation offered by the proposed satellite 2 × 2 MIMO di-versity system. In this regard, a propagation-based analy-sis is performed which is quite different from conventionalcommunication-oriented approaches followed in standardMIMO theory [1]. Specifically, the effect of rainfall on theinterference analysis is taken into account and the differentialrain attenuation related to an adjacent satellite is consideredas the dominant cause of the SIR degradation [22]. Such aninterference problem is further aggravated due to the spa-tial inhomogeneity of the rainfall medium. It constitutes atypical interference scenario, especially over congested urbanareas, where the increased demand for link capacity and ra-dio coverage imposes the coexistence of many satellite radiolinks over the same geographical and spectral area. In the fol-lowing, an analytical prediction model is presented, which


S1 S3 S2

d1,AR1

d3,AR3 d2,AR2

Δθ

Δψ

TS

(a)

To S1

To S3

To S2

ϕ3ϕ2

ϕ1

TS

(b)

Figure 4: (a) Configuration of the satellite 2 × 2 MIMO diversity system assumed and the interference scenario on its forward link, (b)associated elevation angles.

quantifies the adjacent satellite CCI mitigation achieved bythe proposed 2 × 2 MIMO system with respect to the corre-sponding SISO one.

Figure 4 depicts the configuration of the assumed inter-ference scenario on the forward link of a satellite 2×2 MIMOdiversity system operating at the Ku-band and above andemploying receive antenna selection. The satellites S1 andS2 constitute the dual-satellite transmit part of the MIMOsystem also depicted in Figure 1. Another cochannel satellite(denoted by S3), which may belong to either the same or toanother satellite network, is close in orbit to S1. Thus, CCIproblems may arise on the forward link of the 2 × 2 MIMOsatellite system. S1 and S3 subtend an angle Δψ to TS. Thelength of the slant path S3-TS is denoted by d3, while its ele-vation angle is φ3. The RV associated with the rain inducedattenuation along the interfering path S3-TS (in dB) is de-noted by AR3.

Due to selection diversity at the TS receiver, the antennawith the maximum SNR is selected. In mathematical terms,the same statement is expressed as

SNRout = max{

SNR1, SNR2}⇐⇒ Aout = min

{A1,A2

},

(13)

where SNRi = SNRCSi − ARi (i = 1, 2) is the SNR at each TSantenna under rain fades and Ai (i = 1, 2) the total path lossalong each Si-TS link (i = 1, 2). SNRout corresponds to Aout

which determines the output of the selection combiner at ev-ery instant. The proposed scheme requires only the knowl-edge of the wanted signals’ channels at the receiver, whereasknowledge of the interferer’s channel is not necessary. More-over, no CSI is required at the transmit side. If Md denotesthe diversity system margin associated with the system avail-ability pavail (see the appendix), the satellite MIMO diversitysystem is considered available when the probabilistic event

Ω = (Aout < Md)

(14)

is true. Assuming that

Ωi =(Ai < Md,Ai < Aj

) ((i, j) = (1, 2), (2, 1)

)(15)

denotes the event that “the TS is serviced by the correspond-ing satellite Si (i = 1, 2),” it becomes clear that, due to selec-tion diversity,

Ω = Ω1 ∪Ω2,

Ω1 ∩Ω2 = ∅. (16)

Therefore, the probability that the system is available (see theappendix) can be expressed as

P(Ω) = P(Ω1)

+ P(Ω2). (17)

While the satellite 2 × 2 MIMO diversity system is avail-able (i.e., when either Ω1 or Ω2 are true), it might suffer fromCCI originating from the adjacent satellite S3. If SIRd and rddenote the SIR and the minimum acceptable SIR thresholdof the MIMO diversity system, respectively (both measuredat the output of the TS selection combiner), the probabilityof the event that “the system is interfered while being avail-able” can be mathematically expressed based on the aboveconsiderations as

UIPd = P(SIRd < rd,Ω

)

= P(SIRd1 < rd,Ω1

)+ P

(SIRd2 < rd,Ω2

)

= P1 + P2,

(18)

where UIPd is the so-called unacceptable interference proba-bility (UIP) [23, 24], and the quantities SIRdi (i = 1, 2) areexpressed (in dB) as

SIRd = SIRdi = SIRCSi − ARi + AR3 (i = 1, 2). (19)

In (19), SIRCSi (i = 1, 2) is the nominal SIR value underclear sky conditions. In propagation terminology, ARi − AR3


(i = 1, 2) is known as the differential rain attenuation (DRA)[22]. Based on (19), when DRA becomes sufficiently largedue to the spatial inhomogeneity of the rainfall medium, se-vere CCI problems may arise aggravating the SIRd distribu-tion on the forward link of the proposed satellite 2×2 MIMOdiversity system. To this end, UIPd is proposed as an efficientmetric to deal with the statistical behaviour of the SIRd and,together with rd, they constitute a pair of design specifica-tions concerning interference. Every user must comply withthese specifications, given the QoS specified by the event Ωrelated to the system availability (see the appendix).

The quantities SIRCSi (i = 1, 2) encountered in (19) aregiven by

SIRCSi = SIR∗i −GR(θi)

(i = 1, 2), (20)

where θi (i = 1, 2) are the off-axis angles formed by the in-terfering link S3-TS and the wanted links Si-TS (i = 1, 2) inthe radiation pattern of the TS antennas. From Figure 4, itfollows that θ1 = Δψ and θ2 = Δθ − Δψ. Also, in (20), SIR∗i(i = 1, 2) are the relevant SIR values of the interfered linksSi-TS (i = 1, 2) when θi = 1◦, and correspond to the nominalCCI levels. Based on the channel model assumed, their inter-relationship is defined through (6) by simply substituting theSNRCSi by SIR∗i .

Extending the transformation given in (8) to include alsothe interfering link S3-TS (i.e., for i = 1, 2, 3) and making thechannel modeling assumptions, the probabilities Pi (i = 1, 2)encountered in (18) after some straightforward algebra areevaluated, that is,

Pi =∫ uDi

uCidu1

∫ +∞

u1

du2 fU1U2

(u1,u2

)

×[

1− 12

erfc(uEi − μ3/1,2√

2σ3/1,2

)](i = 1, 2),

(21)

where fU1U2 (u1,u2) is the pdf of the two-dimensional jointnormal distribution.

For i = 1, 2, the rest of the parameters encountered in(21) are

uCi =[

ln(xdi)− ln

(AmRi

)]

SaRi,

xdi =

⎧⎪⎪⎨

⎪⎪⎩

0, rd > SIRCSi,(SIRCSi−rd

)cosφi, SIRCSi +FSLi−Md<rd≤SIRCSi,

(Md − FSLi

)cosφi, rd ≤ SIRCSi + FSLi −Md,

uDi =[

ln((Md − FSLi

)cosφi

)− ln(AmRi

)]

SaRi,

uEi =[

ln((

exp(uiSaRi

)AmRi

cosφi− SIRCSi + rd

)cosφ3

)

− ln(AmR3

)]/SaR3 .

(22)

AmRi , SaRi (i = 1, 2, 3) are analytically given in (12). Fur-thermore, μ3/1,2 and σ3/1,2 are the statistical parameters ofthe conditional distribution of the normal RV u3 given

the other two normal RVs u1, u2 and can be expressed interms of the logarithmic correlation coefficients ρni j((i, j) =(1, 2), (1, 3), (2, 3)) as [17, 27]

μ3/1,2 = ρn13 − ρn12ρn23

1− ρ2n12

u1 +ρn23 − ρn12ρn13

1− ρ2n12

u2,

σ23/1,2 =

1− ρ2n12 − ρ2

n13 − ρ2n23 + 2ρn12ρn13ρn23

1− ρ2n12

.

(23)

5. NUMERICAL RESULTS AND DISCUSSION

The previous analyses have been applied for the predictionof possible capacity improvement and interference mitiga-tion achieved by the proposed satellite 2 × 2 MIMO spa-tial multiplexing and diversity systems, respectively, and forcomparison to the relevant SISO cases. To this end, the base-line configuration scenario considers a TS located in At-lanta, GA, and communicating with geostationary satellitesS1(φ1 = 45◦) and S2(φ2 = 40◦). The angular separation as-sumed is Δθ=40◦, which results in a spatial correlation coef-ficient of rain attenuation ρ12 = 0.6 (see Figure 3). Moreover,regarding the interference scenario, an adjacent geostation-ary satellite S3(φ3 = 45◦), separated from S1 by Δψ=10◦, isconsidered to cause CCI problems on the forward link of thesatellite 2× 2 MIMO diversity system.

First, the validity of the proposed analytical model in (9),predicting the outage capacity achieved by a satellite 2 × 2MIMO spatial multiplexing system, is numerically verified.The effect of various geometrical and operational system pa-rameters on the outage capacity distribution is also exam-ined.

Figure 5 shows the dependence of the 1% outage capac-ity of the assumed 2× 2 MIMO satellite system on the SNR.4

The baseline configuration scenario is adopted, whereas theoperating frequency band assumed is Ka (i.e., f = 20 GHz).For the sake of comparison, the capacity of the relevant SISOsystem is also plotted. Together with the analytical resultsobtained from the analytical closed form expression in (9),Monte Carlo simulation results are also plotted for verifica-tion. The agreement observed between the analytical and thesimulation results is very good over the whole SNR range.As can be seen, the difference between the relevant MIMOand SISO curves diminishes at very low SNR levels whileit becomes significant as the SNR increases. As an illustra-tion, for SNR = 10 dB, the spectral efficiency achieved bythe MIMO system is 4.84 bps/Hz, whereas the one achievedby the SISO system is 3.23 bps/Hz. This constitutes, approx-imately, a 50% increase in user data rate obtained by MIMOspatial multiplexing. For SNR = 20 dB, the respective per-formance figures obtained are 10.95 bps/Hz and 6.41 bps/Hzcorresponding to, approximately, a 71% increase in user data

4 Note that the clear sky SNR of strong eigenmode, SNRCS1, has been par-ticularly considered. However, due to the enormous slant path lengths as-sociated, the resulting difference between SNR CSi (i = 1, 2) is minimumsee (6) and, therefore, any of the two SNRCSi can be used as x-coordinates.


0 5 10 15 20 25 30

SNR (dB)

0

2

4

6

8

10

12

14

16

18

1%ou

tage

capa

city

(bps

/Hz)

Analytical expression (9)

Monte Carlo simulation

2× 2 MIMO

SISO

Figure 5: 1% outage capacity versus SNR for a satellite 2×2 MIMOspatial multiplexing system. Relevant SISO case is also plotted forcomparison. Verification of analytical closed form expression in (9)through Monte Carlo simulation.

0 5 10 15 20 25 30

SNR (dB)

0

2

4

6

8

10

12

14

16

18

Ou

tage

capa

city

ach

ieve

dby

2×

2M

IMO

syst

em(b

ps/H

z)

q = 1%, Δθ = 40◦, Ka-band, Atlantaq = 0.1%, Δθ = 40◦, Ka-band, Atlantaq = 1%, Δθ = 40◦, Ku-band, Atlanta

q = 1%, Δθ = 40◦, Ka-band, Singaporeq = 1%, Δθ = 60◦, Ka-band, Atlanta

Figure 6: Outage capacity versus SNR for a satellite 2 × 2 MIMOspatial multiplexing system. Effect of capacity outage probability q,angular separation Δθ, operating frequency f , and climatic condi-tions over the serviced area.

rate. Therefore, the capacity gain obtained by the proposedsatellite 2 × 2 MIMO spatial multiplexing system over theSISO system turns out to be significant for no additionaltransmit power or bandwidth expenditure.

Figure 6 shows the dependence of the outage capacityachieved by a satellite 2 × 2 MIMO spatial multiplexing sys-

tem on the SNR, the angular separation Δθ, the operatingfrequency f , the capacity outage probability q, and the cli-matic conditions over the serviced area. All the results pre-sented here have been obtained employing (9). The baselineconfiguration scenario is adopted. The rest of the relevant pa-rameters assumed as well as the deviations from the baselinescenario are indicated on Figure 6. As can be seen, as either qdecreases or f increases or as the rain conditions over the ser-viced area become heavier, the rain fading becomes more se-vere and, therefore, the outage capacity achieved by the 2× 2MIMO satellite system decreases. Moreover, as the angularseparation Δθ increases (from 40◦ to 60◦), the spatial corre-lation coefficient due to rainfall medium ρ12 decreases cor-respondingly (from 0.6 to 0.5, see Figure 3), and the outagecapacity achieved increases.

In the following, the proposed analytical model in (21)predicting the interference mitigation achieved by a satellite2 × 2 MIMO diversity system with receive antenna selectionis numerically verified. The effect of various geometrical andoperational system parameters on the forward link SIR dis-tribution is also examined.

Figure 7 shows the dependence of the UIP of the assumed2 × 2 MIMO satellite system on the SIR, the system avail-ability pavail, and the operating frequency band. Particularly,two different values of system availability, pavail = 99.9%and 99.99%, and two different operating frequencies, f =12 GHz and 20 GHz, are assumed. For the sake of compar-ison, the UIP of the relevant SISO systems is also plotted.The baseline configuration scenario is adopted. The nomi-nal CCI level assumed is SIR∗1 = 20 dB, whereas the rest ofthe parameters encountered in the interference analysis areindicated on Figure 7. It is obvious that, due to rain, an SIRdegradation is observed for the same UIP level, which be-comes more severe as either pavail or f increases. This fur-ther indicates that satellite systems operating at higher avail-abilities or at higher-frequency bands are more sensitive tointerference. The SIR improvement achieved by the satellite2 × 2 MIMO diversity system over the SISO one is signifi-cant, especially for high pavail and high f . As an illustration,for UIP = 0.001%, the interference mitigation obtained is0.67 dB at the Ka-band and for a 99.9% availability, 1.60 dBat the Ku-band and for a 99.99% availability, and 3.52 dB atthe Ka-band and for a 99.99% availability.

Figure 8 quantifies the SIR improvement achieved by asatellite 2 × 2 MIMO diversity system employing receiveantenna selection with respect to the relevant SISO one.Specifically, the difference (in dB) between the respectiveSIR thresholds achieved at the TS receiver input for UIP =0.001% is plotted versus the angular separation Δθ. Twoareas with different climatic conditions are considered, At-lanta, GA, and Athens, Greece. The operating frequency, sys-tem availability, and nominal CCI level assumed are 20 GHz,99.99%, and SIR∗1 = 20 dB, respectively, while the rest ofthe parameters are the same as those of the baseline con-figuration scenario. As Δθ increases, the interference miti-gation level achieved becomes higher. Moreover, it can easilybe observed that the SIR improvement obtained in Atlanta,


2 4 6 8 10 12 14 16 18 20

SIR (dB)

10−6

10−5

10−4

10−3

10−2

10−1

100

Un

acce

ptab

lein

terf

eren

cepr

obab

ility

(UIP

)

SISO2× 2 MIMO

Ka-band,pavail = 99.9%

Ku-band,pavail = 99.99%

Ka-band,pavail = 99.99%

Figure 7: UIP versus SIR for a satellite 2 × 2 MIMO diversity sys-tem employing receive antenna selection. Relevant SISO case is alsoplotted for comparison. Effect of system availability pavail, operatingfrequency f , and rain climatic conditions over the serviced area.

20 30 40 50 60 70 80 90

Angular separation, Δθ (deg)

0

0.5

1

1.5

2

2.5

SIR

impr

ovem

ent

ach

ieve

dth

rou

ghM

IMO

dive

rsit

y(d

B)

Atlanta, GA

Athens, GR

Figure 8: SIR improvement achieved by a satellite 2× 2 MIMO di-versity system with receive antenna selection over the relevant SISOsystem versus angular separation Δθ. Effect of rain climatic condi-tions over the serviced area.

GA, is much higher than that in Athens, Greece, due to thecorresponding heavier rain conditions.

For various obvious reasons, there is a tendency to placesatellites in orbit close to each other. Due to the increasedCCI, adjacent satellite networks cannot usually operate un-der certain SIR specifications. The proposed MIMO diversitysystem may overcome this problem by adequately increasingSIR in the presence of adjacent CCI. To demonstrate this, asatellite 2 × 2 MIMO diversity system together with its rele-vant SISO case are considered in Figure 9. The input parame-

7 9 11 13 15 17 19 20

SIR (dB)

10−6

10−5

10−4

10−3

10−2

10−1

100

Un

acce

ptab

lein

terf

eren

cepr

obab

ility

(UIP

)

SISO2× 2 MIMO

Δψ = 4◦ Δψ = 5◦

Figure 9: UIP versus SIR for a satellite 2 × 2 MIMO diversity sys-tem employing receive antenna selection. Relevant SISO case is alsoplotted for comparison. Effect of angular separation ΔΨ.

ters assumed are the same as those in the baseline configura-tion scenario, with the exception of a different angular sepa-ration Δψ, that is, Δψ = 5◦ is now assumed. Operation of thesystem at the Ka-band and for a 99.99% availability is con-sidered. To obtain the necessary QoS for UIP = 0.001%, sup-pose that an SIR threshold of 10 dB must be overcome. In theSISO case, when the angular separation between the wantedsatellite S1 and the adjacent interfering one S3 is Δψ = 5◦,an SIR level of 11.2 dB is obtained for UIP = 0.001%, thussatisfying the QoS requirement. If the interfering satellite S3

is closer in orbit to S1, so that their angular separation is re-duced to Δψ = 4◦, the SIR level in the SISO case falls downto 9.8 dB, thus failing to satisfy the QoS requirement. Em-ploying the proposed 2 × 2 MIMO satellite system, the SIRachieved when Δψ = 4◦ is 11.32 dB, thus remaining abovethe QoS threshold. This is another advantage of the proposedsatellite MIMO diversity system, allowing the closer installa-tion of satellites in orbit.

6. CONCLUSIONS

In this paper, the applicability of MIMO technology to satel-lite communication systems operating at the Ku-band andabove is investigated. Emphasis is put on satellite diversity asa potential candidate to form a MIMO matrix channel in thesatellite environment. The relevant propagation phenomenaat the frequencies of interest have been considered throughan appropriate physical channel model, which takes into ac-count clear LOS operation, high antenna directivity at the TSreceiver, the effect of rain fading, and the slant path lengthsdifference. Also, as it may accept physical inputs from theITU-R rainmaps, it is flexible and can be applied on a globalscale.


Useful analytical results are presented for two differentapplications of MIMO technology:

(i) capacity improvement in a satellite 2×2 MIMO spatialmultiplexing system,

(ii) interference mitigation in a satellite 2 × 2 MIMO di-versity system with receive antenna selection.

In the first application, significant capacity gains of theMIMO system over the relevant SISO one are demonstrated,especially for moderate and high SNR levels. The practicalcase when no CSI is available at the transmitters of the twoindividual satellites is considered. A useful closed form ex-pression for the outage capacity achieved by 2 × 2 MIMOsatellite systems is provided and successfully verified throughMonte Carlo simulations. Such an expression is extremelyhard to obtain even in the well-established field of MIMOtheory, is applicable over a large SNR range, and can incorpo-rate the effect of various geometrical and operational systemparameters on the outage capacity distribution.

In the second application, the receive antenna selectionscheme employed in the satellite MIMO system assumed isconsidered to counteract CCI problems over its forward link.SIR gain of several dB is demonstrated in the numerical re-sults. An analytical propagation model for the calculation ofthe interference mitigation achieved is presented, which isflexible and can incorporate the influence of various geomet-rical and operational system parameters on the SIR distribu-tion.

APPENDIX

CALCULATION OF SATELLITE 2× 2 MIMODIVERSITY SYSTEM MARGIN Md

Every user in the assumed satellite 2×2 MIMO diversity sys-tem employing receive antenna selection must comply with acertain availability percentage pavail related to a diversity sys-tem margin Md:

pavail · 100% = P(Ω) = P(Aout < Md

)

= P(min

{A1,A2

}< Md

)

= 1− P(A1 > Md,A2 > Md)

= 1− P(AR1 > Md − FSL1,AR2 > Md − FSL2).

(.1)

Considering the transformation given in (8), relating the log-normal rain attenuation RVs ARi (i = 1, 2) to the normalizednormal RVs ui (i = 1, 2), and the channel modeling assump-tions, pavail is expressed as

pavail · 100% = 1−∫ +∞

uF1

du1

∫ +∞

uF2

du2 fU1U2

(u1,u2

), (.2)

where

uFi =[

ln((Md − FSLi

)cosφi

)− ln(AmRi

)]

SaRi(i = 1, 2).

(.3)

After straightforward algebra, (.2) yields

pavail · 100%

= 1− 0.5∫ +∞

uF1

du1 fU1

(u1)

erfc

(uF2 − ρn12u1√

2(1− ρ2

n12

)

)

.(.4)

ACKNOWLEDGMENTS

The authors are indebted to the three anonymous review-ers whose constructive comments helped to significantly im-prove the initial version of this paper. Moreover, the first au-thor would like to thank Professor Bhaskar D. Rao from Uni-versity of California, San Diego, USA, for the fruitful discus-sions they had on the first part of this work.

REFERENCES

[1] A. J. Paulraj, D. A. Gore, R. U. Nabar, and H. Bolcskei, “Anoverview of MIMO communications—a key to gigabit wire-less,” Proceedings of the IEEE, vol. 92, no. 2, pp. 198–218, 2004.

[2] D. Gesbert, M. Shafi, D.-S. Shiu, P. J. Smith, and A. Naguib,“From theory to practice: an overview of MIMO space-timecoded wireless systems,” IEEE Journal on Selected Areas inCommunications, vol. 21, no. 3, pp. 281–302, 2003.

[3] A. D. Panagopoulos, P.-D. M. Arapoglou, and P. G. Cottis,“Satellite communications at Ku, Ka, and V bands: propaga-tion impairments and mitigation techniques,” IEEE Commu-nications Surveys and Tutorials, vol. 6, no. 3, pp. 2–14, 2004.

[4] K. P. Liolis, A. D. Panagopoulos, and P. G. Cottis, “Outage ca-pacity statistics of MIMO satellite networks operating at Kaband and above,” in Proceedings of the 12th Ka and BroadbandCommunications Conference, Naples, Italy, September 2006.

[5] F. Yamashita, K. Kobayashi, M. Ueba, and M. Umehira,“Broadband multiple satellite MIMO system,” in Proceedingsof the 62nd IEEE Vehicular Technology Conference (VTC ’05),pp. 2632–2636, Dallas, Tex, USA, September 2005.

[6] P. R. King and S. Stavrou, “Land mobile-satellite MIMO ca-pacity predictions,” Electronics Letters, vol. 41, no. 13, pp. 749–751, 2005.

[7] T. Hult and A. Mohammed, “MIMO antenna applicationsfor LEO satellite communications,” in Proceedings of the 3rdESA International Workshop of the European COST 280 Action,Prague, Czech Republic, June 2005.

[8] C. Martin, A. Geurtz, and B. Ottersten, “Spectrally efficientmobile satellite real-time broadcast with transmit diversity,”in Proceedings of the 60th IEEE Vehicular Technology Confer-ence (VTC ’04), vol. 6, pp. 4079–4083, Los Angeles, Calif, USA,September 2004.

[9] C. Faller, B.-H. Juang, P. Kroon, H.-L. Lou, S. A. Ramprashad,and C.-E. W. Sundberg, “Technical advances in digital audioradio broadcasting,” Proceedings of the IEEE, vol. 90, no. 8, pp.1303–1333, 2002.

[10] J. Mietzner and P. A. Hoeher, “Distributed space-time codesfor cooperative wireless networks in the presence of differentpropagation delays and path losses,” in Proceedings of SensorArray and Multichannel Signal Processing Workshop (SAM ’04),pp. 264–268, Barcelona, Spain, July 2004.

[11] B. N. Getu and J. B. Andersen, “The MIMO cube—a compactMIMO antenna,” IEEE Transactions on Wireless Communica-tions, vol. 4, no. 3, pp. 1136–1141, 2005.


[12] I. Frigyes and P. Horvath, “Polarization-time coding in satel-lite links,” IEEE Satellite and Space Communications Newsletter,vol. 15, no. 2, pp. 6–8, 2005.

[13] P. Horvath and I. Frigyes, “SAT02-6: application of the3D polarization concept in satellite MIMO systems,” inProceedings of IEEE Global Telecommunications Conference(GLOBECOM ’06), pp. 1–5, San Francisco, Calif, USA,November 2006.

[14] P. R. King and S. Stavrou, “Capacity improvement for a landmobile single satellite MIMO system,” Antennas and WirelessPropagation Letters, vol. 5, no. 1, pp. 98–100, 2006.

[15] M. Sellathurai, P. Guinand, and J. Lodge, “Space-time cod-ing in mobile satellite communications using dual-polarizedchannels,” IEEE Transactions on Vehicular Technology, vol. 55,no. 1, pp. 188–199, 2006.

[16] G. Taricco, E. Viterbo, and E. Biglier, “MIMO transmission formobile satellite communication systems: a review,” in Proceed-ings of the 8th International Workshop on Signal Processing forSpace Communications (SPSC ’03), Catania, Italy, September2003.

[17] A. D. Panagopoulos and J. D. Kanellopoulos, “Prediction oftriple-orbital diversity performance in Earth-space commu-nication,” International Journal of Satellite Communications,vol. 20, no. 3, pp. 187–200, 2002.

[18] ITU-R Recommendation P.837-4, “Characteristics of Precipi-tation for Propagation Modeling,” Geneva, Switzerland, 2003.

[19] G. J. Foschini and M. J. Gans, “On limits of wireless commu-nications in a fading environment when using multiple an-tennas,” Wireless Personal Communications, vol. 6, no. 3, pp.311–335, 1998.

[20] I. E. Telatar, “Capacity of multi-antenna Gaussian channels,”European Transactions on Telecommunications, vol. 10, no. 6,pp. 585–595, 1999.

[21] S. Sanayei and A. Nosratinia, “Antenna selection in MIMO sys-tems,” IEEE Communications Magazine, vol. 42, no. 10, pp. 68–73, 2004.

[22] J. D. Kanellopoulos, S. Ventouras, and C. N. Vazouras, “A re-vised model for the prediction of differential rain attenua-tion on adjacent Earth-space propagation paths,” Radio Sci-ence, vol. 28, no. 6 part 2, pp. 1071–1086, 1993.

[23] P.-D. M. Arapoglou, A. D. Panagopoulos, J. D. Kanellopou-los, and P. G. Cottis, “Intercell radio interference studies inCDMA-based LMDS networks,” IEEE Transactions on Anten-nas and Propagation, vol. 53, no. 8, pp. 2471–2479, 2005.

[24] A. D. Panagopoulos, P.-D. M. Arapoglou, J. D. Kanellopoulos,and P. G. Cottis, “Intercell radio interference studies in broad-band wireless access networks,” IEEE Transactions on VehicularTechnology, vol. 56, no. 1, pp. 3–12, 2007.

[25] ITU-R Recommendation S.580-6, “Radiation Diagrams forUse as Design Objectives for Antennas of Earth Stations Op-erating with Geostationary Satellites,” Geneva, Switzerland,2004.

[26] P. Horvath and I. Frigyes, “Application of the MIMO conceptin millimeter-wave broadband wireless access networks,” In-ternational Journal of Wireless Information Networks, vol. 11,no. 4, pp. 217–225, 2004.

[27] A. Papoulis and S. U. Pillai, Probability, Random Variables andStochastic Processes, McGraw-Hill, Englewood Cliffs, NJ, USA,4th edition, 2002.


Research ArticleInvestigations in Satellite MIMO Channel Modeling:Accent on Polarization

Peter Horvath,1 George K. Karagiannidis,2 Peter R. King,3 Stavros Stavrou,3 and Istvan Frigyes1

1 Department of Broadband Infocommunications and Electromagnetic Theory, Budapest University of Technology and Economics,H-1111 Budapest, Hungary

2 Division of Telecommunications, Department of Electrical and Computer Engineering, Aristotle University of Thessaloniki,54124 Thessaloniki, Greece

3 Centre for Communication Systems Research, University of Surrey, Guildford, Surrey GU2 7XH, UK

Received 30 September 2006; Accepted 19 March 2007

Recommended by Ray E. Sheriff

Due to the much different environment in satellite and terrestrial links, possibilities in and design of MIMO systems are ratherdifferent as well. After pointing out these differences and problems arising from them, two MIMO designs are shown rather welladapted to satellite link characteristics. Cooperative diversity seems to be applicable; its concept is briefly presented without a de-tailed discussion, leaving solving particular satellite problems to later work. On the other hand, a detailed discussion of polarizationtime-coded diversity (PTC) is given. A physical-statistical model for dual-polarized satellite links is presented together with mea-suring results validating the model. The concept of 3D polarization is presented as well as briefly describing compact 3D-polarizedantennas known from the literature and applicable in satellite links. A synthetic satellite-to-indoor link is constructed and its elec-tromagnetic behavior is simulated via the FDTD (finite-difference time-domain) method. Previous result of the authors states thatin 3D-PTC situations, MIMO capacity can be about two times higher than SIMO (single-input multiple-output) capacity while adiversity gain of nearly 2× 3 is further verified via extensive FDTD computer simulation.

Copyright © 2007 Peter Horvath et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1. INTRODUCTION

It is more or less a commonplace statement that in the wire-less technology of recent years, systems applying multiple-transmit and multiple-receive antennas (MIMO, multiple-input multiple-output) have become one of the few meth-ods of real innovation. Space-time processing, in particularspace-time coding (STC) techniques as applied to MIMOsystems in a multipath environment, results in significantimprovement both in transmission capacity and reliability.It turns out that there are significant differences between ter-restrial and satellite multipath channels; these result in signif-icant differences in MIMO applications as well. In this paper,we deal with some special problems raised by special charac-teristics of satellite links.

In terrestrial applications of MIMO, the basic methodto diversify channels is with the additional dimension ofspace, that is, antennas are displaced spatially from eachother, resulting in space-time processing. In addition, multi-path channels and relevant fading characteristics—Rayleigh,Rice, Suzuki, and so forth—are assumed. A similar situation

is present in satellite-to-mobile or satellite-to-indoor links.Among others, in [1] it is experimentally verified that theLEO satellite-to-indoor channel has nearly exactly Rayleighcharacter at any fixed indoor spot. More precise models areavailable (Loo, Corrazza, etc.) well describing the multipathbehavior and not differing much from the terrestrial case.Consequently, similar-to-terrestrial results can be foreseen insatellite links of appropriate design. However, due to the veryhuge length of the radio path, transmit and/or receive anten-nas must be placed at significant distances from each otherin order to ensure that the various paths are really diverse.To achieve this in principle generalization of satellite diver-sity and site diversity would be candidates in forming MIMOchannels. (Note that in satellite diversity, there are two ormore satellites transmitting/receiving the same signal; in sitediversity there are two or more Earth stations.) These wouldmake original space time processing possible: both groundand satellite terminals are in this case remote from each otherand so are their antennas. Of course the original concept ofsite diversity can be excluded in the present—mostly hand-held mobile/indoor—situations.


In one class of cases, the ground terminals are located on-board large objects, such as trains, ships, or aircrafts. Large-antenna distances are possible then, realizing diverse routes.Multipath, on the other hand, is nonexistent or very sparse.Difference of LOS route lengths must be in such a case atleast λ/16 · · · λ/4. Site diversity might be applicable then, ifas a rough estimate, terminal antennas can be placed at adistance of b = 35 m from each other. (For that figure, anLEO satellite and 30 GHz carrier frequency were assumed;note that b is proportional to the square root of satellitedistance×wavelength.)

Satellite diversity for space-time processing would fulfillthe requirement of uncorrelated channels and so it would beapplicable. There is a few papers dealing with this topic; forexample, [2] gives a physical-statistical model for satellite-to-urban and satellite-to-highway channel and computes capac-ity of a 2×2 MIMO system. In [3], a satellite-diversity MIMOsystem and its system aspects are investigated. Further paperson satellite MIMO are, among others, [4, 5].

There exists, however, at least one problem not presentin terrestrial systems, that is, that of synchronization. In ter-restrial MIMO systems, both the group of transmit anten-nas and that of receive antennas are at distances from eachother in the order of a wavelength. Consequently, the pathlengths of the diversity routes are very closely identical, andthus signals arriving from the transmitter to the receiver aresynchronous. This makes identification and decoding of thereceived signals rather easy. In the case of satellite diversity,the satellites serving as diversity terminals are very far fromeach other. Thus difference of path lengths and so delays be-tween the satellites and the ground terminal can be very highand highly variable. (This variability is self-evidently existingin the case of LEO satellites but very likely also in the GEOcase.) As a consequence, the arrival time of signals from twosatellites (forming part of a single code word) can be shiftedby tens or hundreds of symbol times relative to each other.Synchronization of the received signals is in this case rathercomplicated—both acquisition and tracking. Reference [2]or [3] or other satellite/MIMO papers known by the authorsdo not deal with this problem. General aspects of it are dealtwith, for example, in [6–8], taking explicitly, however, short-range, that is, terrestrial situations only into account.

An alternative possible solution could be cooperativesatellite diversity (CSD). In general, cooperative relaying sys-tems have a source node (e.g., a terrestrial mobile terminal(TMT)) multicasting a message to a number of cooperativerelays (satellites (SAT)), which in turn resend a processed ver-sion to the intended destination node (another TMT). Thedestination node combines the signal received from the re-lays, possibly also taking into account the source’s originalsignal. Recently, it has been shown that cooperative diversitysystems provide an effective way of improving spectral andpower efficiencies of the wireless networks without the ad-ditional complexity of multiple antennas [7–11]. However, astudy on CSD systems, where the relays are satellites, to thebest of the authors’ knowledge does not exist in the literature.

A third possible method is to apply compact antennas,in which case the synchronization problem is nonexistent.

Compact antennas with low radiator spacing and dimensionsas small as λ/20 or so are described, for example, in [12–14]. These antennas were mainly developed for applicationin handheld terminals, in which the available space is verylimited. In the case of onboard antennas, the whole antennaneed not be small, however, the radiator elements need to becolocated, that is, their ports need to be very close to eachother. Note that polarization, and in many cases the 3D char-acter of it, has a significant role in each of the known compactantennas.

In this paper, the concept of cooperative satellite diversityis briefly introduced, without, however, a detailed discussion;this is done in Section 2. Polarization diversity and the appli-cation of space-time coding concepts in polarization diver-sity are dealt with in Section 3. (In analogy to the name STC,we call that polarization time coding (PTC). Note that ac-cording to the authors’ understanding, the term STC is usedto distinguish a transmit-and-receive-space-diversity situa-tion from a simple receive diversity. The same understandingis applied in this paper; so we will call our topic PTC even ifparticular coding problems are not at all dealt with but codedsignals are assumed.) Section 3.1 deals with dual-polarizedMIMO channels, stating a physical-statistical model, pre-senting measuring results and validating the model; in thisdiscussion conventional dual-polarized antennas are applied.In Section 3.2, PTC antennas of 3-dimensional polarizationare dealt with, introducing the concept of 3D polarization,presenting a few compact MIMO antennas and showingthe essential difference between terrestrial and satellite linksfrom the point of view of 3D PTC. In Section 4, electro-magnetic simulation results are given; in these it is verifiedthat application of the FDTD method is suitable to investi-gate MIMO channel characteristics of very complex environ-ments; capacity as well as diversity behavior are presented;these verify (at least for the present example) the statementsof Section 3.2 and of the authors’ references [15, 16]. Con-clusions are drawn in Section 5.

2. A FEW WORDS ON COOPERATIVESATELLITE DIVERSITY

In general, cooperative relaying systems have a source node(e.g., TMT) multicasting a message to a number of cooper-ative relays (SAT), which in turn resend a processed versionto the intended destination node (another TMT). The des-tination node combines the signal received from the relays,possibly also taking into account the source’s original signal.An example of a CSD system with two satellite relays is shownin Figure 1.

The idea of merging cooperation with space-time codingresulted in the so-called distributed or cooperative space-timecoding (CSTC). Compared to the conventional space-timecoding with collocated antennas, CSTC can be implementedwhen transmitter and relays share their antennas to create avirtual transmit array.

A possible cooperation scenario is applied for the con-figuration of Figure 1, proposed in [9] as TMT1 communi-cates with SAT1 and SAT2 in a broadcasting mode during

Peter Horvath et al. 3

SAT1

TMT1TMT2

SAT2

Figure 1: A virtual array: 2 satellites and 2 terminals.

the first signaling interval and there is no transmission fromSAT1 or SAT2 to TMT2 within this time interval. In the sec-ond signaling interval, both SAT1 and SAT2 communicatewith TMT2. This scenario assumes perfect knowledge of thechannel fading coefficients at the receiver side of TMT2 andsynchronization as an a priori condition. However, the delaysdue to distance between SAT1 and SAT2 (and the different lo-cal oscillators at SAT1 and SAT2) make cooperative diversityasynchronous in nature.

Several methods have been proposed to apply CSTC, inthe presence of asynchronity between relays (see [17, 18] andreferences therein). However, a theoretical analysis on the ef-fect of the (high) asynchronity in cooperative satellite diver-sity systems does not exist in the literature. Such an analysisis out of the scope of the present paper and is left for furtherstudy.

3. POLARIZATION-TIME CODING IN SATELLITECOMMUNICATIONS

3.1. Physical-statistical model for the dual polarizedLMS MIMO channel

In [19], a basic investigation of PTC was presented, usinga simple theoretical MIMO channel model. It was assumedthat in a multipath environment—of whatever polarizationthe transmit antenna(s) is (are)—the received signal is ofcompletely random polarization, that is, any state of polar-ization is equally likely. With a simulation study, we did showthat applying normal dual-polarized antennas at both ter-minals and transmitting Alamouti-type coded signals [20],there is a 2×1 or 2×2 diversity effect if polarization of the re-ceived signals is fully correlated or completely uncorrelated,respectively. Incidentally, polarization characteristics are de-scribed there via Stokes parameters and related concepts. Inorder to assess the benefits of MIMO techniques applied tomobile satellite links, real channel data or accurate channelmodels are required. In this section, a physical-statistical 2×2dual-polarized MIMO channel model is presented.

3.1.1. Channel model construction

The following dual-polarized physical-statistical LMS MI-MO channel model is an extension to the multiple-satelliteLMS MIMO model presented in [2]. In the present paper, asingle satellite containing right-(RHCP) and left-hand circu-lar polarization (LHCP) antennas communicates with a mo-bile vehicle, also containing RHCP and LHCP antennas. Notethat taking into account the spherical symmetry of polariza-tion states on the Poincare sphere, actual choice of two or-thogonal polarizations does not have too much significance[21].

Channel model construction is described in [2]. Addi-tional insertion of polarization properties is achieved as fol-lows. When the LOS path is unobstructed (clear), simplepath loss is applied to the copolar channels and cross-polarchannels are discarded. When the LOS path is blocked by abuilding (blocked), rooftop diffraction is applied to both theco- and cross-polar channels; the cross-polar component isscaled below the copolar component as observed from mea-sured data. When the LOS path is shadowed by vegetation(tree), attenuation is applied to this path based on the dis-tance traversed through the tree and using a typical attenu-ation factor of −1.3 dB per meter [22]. Similarly, the cross-polar component is scaled below the copolar component.

It is assumed in this model that the LOS paths are fullycorrelated between co- and cross-polar channels, and that thediffuse multipath components are fully uncorrelated betweenco- and cross-polar channels. This simplification is represen-tative of many, but not all, real practical channels; a full pre-sentation of measured satellite MIMO channel correlation isprovided in [23].

The high-resolution time-series data αM,N between eachsatellite antenna M and each mobile antenna N can be de-fined as follows:

αM,N =

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

PM,Ne jkdM,N

+bn∑

i=1

TiΓiPM,N ,iejkdM,N ,i clear co-polar

bn∑

i=1

TiΓiPM,N ,iejkdM,N ,i clear cross-polar

DM,NPM,Ne jkdM,N

+bn∑

i=1

TiΓiPM,N ,iejkdM,N ,i block co-polar

SbDM,NPM,Ne jkdM,N

+bn∑

i=1

TiΓiPM,N ,iejkdM,N ,i block cross-polar

TM,NPM,Ne jkdM,N

+bn∑

i=1

TiΓiPM,N ,iejkdM,N ,i tree co-polar

StTM,NPM,Ne jkdM,N

+bn∑

i=1

TiΓiPM,N ,iejkdM,N ,i tree cross-polar

(1)


where PM,N is the LOS path loss between satellite antenna Mand moving mobile antenna N , k is the wavenumber, n isthe total number of valid scatterers, Ti is the tree attenuationapplied to a reflected contribution from scatterer i, Γi is thecomplex reflection coefficient at scatterer i, PM,N ,i is the pathloss from satellite antenna M to moving mobile antenna Nvia scatterer i, dM,N ,i is the distance between satellite antennaM and moving mobile antenna N via scatterer i, DM,N is theLOS diffraction loss, and TM,N is the LOS tree loss. The termsSb and St account for the attenuation of the cross-polar termsfor blocked and tree-shadowed conditions, respectively andare derived from measured data. The term b is a clutter factorparameter also derived from measurements in each environ-ment.

3.1.2. Measurement campaign

Extensive measurements were carried out in Guildford, UK,where an artificial platform situated on a hilltop (acting asthe satellite), containing directional RHCP and LHCP patchantennas, communicated with a mobile van fitted with om-nidirectional RHCP and LHCP antennas. Further details ofthe experiment are given in [23, 24].

Two of the measured environments were modeled: (a)tree-lined road/highway, characterized by a high likelihoodof dense tree matter at either side of the road with occasionalclearings and occasional two-storey houses beyond the veg-etation, and (b) urban, characterized by densely placed two-to-four-storey buildings and sporadic tree matter.

3.1.3. Model output and validation

The model was optimized by fitting its parameters to themeasured data. The model is capable of producing statisti-cally accurate wideband channel time-series data and first-and second-order statistics. In this paper, the first-orderstatistics of the model are presented showing their validationagainst measured data. Validation of second-order statistics,not relevant to the diversity gain analysis presented below, isa work to be published.

An example of the copolar model output high-resolutionpath loss time-series data is shown in Figure 2. Similar datawere obtained between each mobile antenna and satellite, forboth polarizations.

Data were collected using three samples per wavelengthin the model and measurement campaign, ensuring a sam-pling frequency well over twice the maximum Doppler fre-quency.

The narrowband first-order modeled and measurementdata are compared. Cumulative distribution functions of co-and cross-polar channels for highway and urban environ-ments are shown in Figure 3. The 2×2 dual-polarized MIMOchannel matrix data were also used to estimate the diversitygain from a 1× 2 maximum ratio receive combining system,a 2 × 1 polarization time block code approach [20], and a2× 2 polarization time block code system. An example fromthe highway environment data is shown in Figure 4.

−40

−30

−20

−10

0

10

Rec

eive

dp

ower

(dB

)

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Mobile position (m)

Urban

(a)

−40

−30

−20

−10

0

10

Rec

eive

dp

ower

(dB

)

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Mobile position (m)

Highway

(b)

Figure 2: Example copolar time-series data of model.

3.1.4. A short concluding remark on this model

This model can be used to generate more statistically accu-rate channel data, which can be used to evaluate the perfor-mance of polarization time channel codes and algorithms,and therefore evaluate the capacity and diversity benefits ofMIMO techniques applied to LMS systems. However, it mod-els usual double-polarized channels/systems only, resultingin at most 4-fold diversity gain and 2-fold increase in capac-ity. Taking the generalized 3-dimensional (3D) character ofwave polarization state into account (and applying relevantantennas), diversity gain can be increased. In terrestrial ap-plications, capacity can also be increased, however, as we didshow in [15] and briefly discuss here as well, this is not thecase in satellite links. 3D polarization and its application inPTC will be dealt with in what follows. Note that importantpractical issues, like possible loss of capacity due to polar-ization mismatch, and practical antenna configurations arebeyond the scope of the present paper.

3.2. PTC with 3D polarization satellite antennas

3.2.1. The concept of 3D polarization

Polarization state is characteristic to an electromagneticwave. Plane waves are TEM, that is, electric and magneticfield vectors are in the plane perpendicular to the directionof propagation. Thus, polarization is a 2-dimensional phe-nomenon and 2 orthogonal polarization states exist. 2D po-larization state of a wave, polarization properties of an an-tenna, as well as functioning of conventional polarization di-versity and conventional PTC can well be described by theclassical Stokes parameters. (For details see, e.g., [19, 25] for


0.8

0.9

1

P(f

ade

dept

h<

absc

issa

)

−20 −10 0 10

Power relative to FSL (dB)

Measured copolarMeasured X-polarModeled copolarModeled X-polar

(a)

10−2

10−1

100

P(f

ade

dept

h<

absc

issa

)

−45 −40 −35 −30 −25 −20



(b)

0.8

0.9

1

P(f

ade

dept

h<

absc

issa

)

−20 −15 −10 −5 0



(c)

10−2

10−1

100

P(f

ade

dept

h<

absc

issa

)

−45 −40 −35 −30 −25 −20



(d)

Figure 3: Comparison of modeled and measured cumulative distributions; upper figures: highway channel; lower figures: urban channel.

application. It is also mentioned that Stokes parameters forma 4-vector in a Minkowskian space; their transformation, e.g.,by scatterers or polarization filters, is a Lorentz transforma-tion [26]; these properties, however, are not used in this dis-cussion.)

In the case of multipath propagation (or if the directionof propagation is unknown), wave polarization is a 3D phe-nomenon. In that case, the number of orthogonal polariza-tion states is 3. This can increase the number of orthogo-nal channels to 3 if these are discriminated by polarization


10−6

10−5

10−4

10−3

10−2

10−1

100

Bit

erro

rra

te(B

ER

)

0 10 20 30 40 50 60

Eb/N0 (dB)

No diversityMRRC (1 Tx, 2 Rx)

PTBC (2 Tx, 1 Rx)PTBC (2 Tx, 2 Rx)

Figure 4: Bit error rate curves for highway environment.

only; as far as known by the authors, reference [27] was thefirst drawing the attention of the MIMO community to thisfact. Combining antenna polarization and radiation patternin discriminating channels, this number can be significantlyhigher, as this will be briefly discussed in the following sub-section.

(Note that Stokes parameters together with their symme-try and invariance properties can be generalized to the 3Dcase as well [28]. It is not known by the authors, however,if these were ever applied in MIMO or communication an-tenna problems.)

3.2.2. Compact MIMO antennas

If the degree of asynchronism arising in multisatellite-to-ground links is too high so that synchronization or cooper-ative diversity is not possible or is too complicated, MIMOantennas have to be colocated onboard a single satellite. Thissituation is similar although not identical to handheld termi-nals. Like in that case, space is not an available dimension fordiversifying multiple signals: polarization and antenna pat-tern are only available. It is different on the other hand asavailable space is not as much limited as in the case of hand-held terminals; so the antennas can be large, and aperture orarray antennas of sufficiently high gain can be applied. In re-cent times, there is a significant progress in the field of com-pact multielement antennas. We mention three new struc-tures investigated in the literature.

Reference [12] deals with what is sometimes called avector element antenna. This contains 6 rectangular placedHertzian dipoles, 3 electric and 3 magnetic. Rectangular elec-tric and rectangular magnetic dipoles as well as electricaldipoles parallel to magnetic are fully uncorrelated, while rect-angular placed electric to magnetic dipoles are of zero or ofvery low correlation; the latter is due to different angular pat-terns. Thus in the case of very rich scattering environment,

6-fold receive diversity gain can be achieved or in principleeven 6 × 6 diversity gain if both the transmitter and the re-ceiver operate with vector element antennas. Increase in ca-pacity, however, cannot be more than 4-fold, as shown by[29].

In [13], the so-called MIMO cube is dealt with. This con-tains 12 electric dipoles arranged at the edges of a cube.Cube-to-cube capacity and other parameters are computed,showing surprisingly good performance; note, however, thateven very small cubes are investigated, (cube edges as short as0.05λ) the problem of superdirectivity is not stressed in thatpaper.

In [14], behaviors of three colocated monopole anddipole antennas are investigated, versus their mutual angles,via simulation. It is shown that their performance is veryclose to ideally orthogonal ones and also that the main causeof achieving that is their different polarizations rather thandifferent angular patterns.

3.2.3. Compact antennas and 3D polarization in satellites

There is a significant difference between the environmentof a terrestrial multipath link and a satellite multipath link.In Figure 5, terrestrial multipath links for indoor or mo-bile communication are schematically shown. The system de-picted in Figure 5(a) is of double-bounce scattering, whereasthat of Figure 5(b) is of single bounce. “Compact anten-nas” are used in both terminals—as an example realized inthe form of triple dipoles. It is self-evident from Figure 5(a)that waves are arriving to the receive antenna from multipledirections—resulting in three orthogonal polarization com-ponents. But the case is similar in situations like Figure 5(b);this is due to the relatively short distance—characteristic interrestrial, in particular in indoor links.

A satellite-to-indoor/mobile link, shown in Figure 6, ismuch different, as in this case terminals are (i) very far fromeach other and (ii) scatterers are very far from one of these.Due to (i), antenna must be of high gain, shown in the figureas an aperture. And, due to (ii), TEM waves travel betweenthe satellite and the neighborhood of the ground terminal.Propagation is multipath only in that—relatively short—distance. The aperture itself can be realized either as a dishor as an array. It could be illuminated by any 3D polarizedwave, however, only the 2D component of that would traveltowards the ground terminal.

Based on this fact, we have shown in [15] that in a satel-lite link relative to the single-channel case, only a 2-fold in-crease of capacity can be achieved by PTC. This is in con-trast to the terrestrial case in which this increase is 4-fold.In more details, while any small multielement antenna canbe applied in the ground terminal, onboard one satellite atmost conventional double-polarized antennas are applicable,or more precisely, are reasonable. On the other hand, diver-sity can take the full advantage of the capabilities of multi-ple antennas if these are applied in the ground terminal. Asa consequence of these, this type of channel is asymmetric:the downlink is a double-input multiple-output channel, theuplink is its inverse, that is, multiple-input double-output.


t(t)

Scatteringmedium

Scatteringmedium

r(t)

(a)

t(t)

Scatteringmedium

r(t)

(b)

Figure 5: Terrestrial multipath links with compact MIMO anten-nas in scattering media; (a) double-bounce scattering; (b) singlebounce.

t(t)

Plane wave

ApertureScatteringmedium

r(t)

Figure 6: A satellite-to-mobile/indoor link.

This has the consequence that from the coding point of view,the system is not uniform. If as an example, space-time blockcoding of the Alamouti type or orthogonal space-time blockcoding (OSTBC) is chosen, RC = 1 can be applied downlink,however in the uplink RC = 1/2 or at most RC = 3/4 canonly be achieved. (RC designates the coding rate.) It is ques-tionable if this can be accepted from the frequency economypoint of view. If not, only two of the three or more antennasare used in the uplink transmitter. Note that other types ofcoding can give different results.

On the other hand, the number of diversity routes isincreased—say up to 2× 3. (This is valid if terminal antennais a tripole; with a vector element antenna, this is 2× 6, witha MIMO cube even 2× 12.)

Incidentwave

Window

O1 O2 O3

y = 4.5 m

x=

2.8

m

Figure 7: A satellite-to-mobile/indoor link.

In the next section, applying electromagnetic simulationwe verify the capacity and the diversity characteristics asstated above.

4. FDTD SIMULATION OFA SATELLITE-TO-INDOOR LINK

In order to assess the performance of using three orthog-onally polarized antennas in a satellite-to-indoor scenario,some simulations were performed using full-wave electro-magnetic tools. The FDTD method [30] was used to calculatethe time-dependent electromagnetic field inside a typical of-fice room where the mobile terminal is assumed to be placed.The office dimensions were 2.8 m × 4.5 m × 3.0 m (x, y, z),where the floor and the ceiling are lying in and parallel to thex-y plane, respectively, as seen in Figure 7. In the simulation,the furniture and the walls of the room are modeled by re-alistic material properties (brick walls, wooden and metallicfurniture, and some plastic objects). These objects of vari-ous geometries are nearly uniformly distributed in the room.Linear orthogonally polarized plane waves enter the roomthrough the window and through the external wall; one po-larization during the first simulation run and the other oneduring a subsequent run. This method allows us to split thechannel response according to the incoming polarizations.The waveform is a modulated Gaussian pulse centered at1.2 GHz, entering through the x-z plane at y = 0 m.

The electric field components (Ex, Ey , and Ez) arerecorded at various spots in the room. We use these fieldcomponents directly to draw conclusions about the signals(voltages) which three antennas would produce if they wouldbe placed at a given observation point. Although this ap-proach does not consider the current distribution on elec-trically long antennas, mutual coupling, scattering by the an-tennas, and so forth, previous FDTD studies demonstratedthat only a very low crosstalk exists between three thin-wirehalf-wave dipoles which are mounted parallel to the coor-dinate axes in an empty room [16]. Therefore, the resultscan be regarded as realistic, for short orthogonally mounteddipoles. The field components are recorded along variousx-z cross-sections of the room, at three different observa-tion planes (O1 at y = 1.5 m, O2 at y = 2.4 m, and O3


at y = 4 m), representing different propagation environ-ments due to different shadowing and angle-of-incidence pa-rameters. At each of the three planes, about 800 points wereobserved, spaced 7.5 cm apart in both x and z directions. In afirst scenario (S1), the incident waves arrive horizontally (at0 elevation and parallel to y-axis). In a second scenario (S2),the elevation was chosen to be 30 degrees and the azimuthangle 20 degrees off the y-axis. Thus, in the latter case, theline of sight is blocked at the points of O2 and O3. For eachscenario, two simulation runs yielded 6 time functions of thefields (Ex, Ey , and Ez when using the one or the other po-larization). From the observed fields, which were regarded asreceived voltages according to the reasoning presented above,signal portions weaker than a designated noise level, chosento be −15 dB relative to the maximum power level, were dis-carded. Then the envelope of the received signals was calcu-lated. Based on these data, three statistical parameters werederived for both Scenarios 1 and 2. First, the equal-powercapacity [31, Equation (4)], was calculated and its CDF wasdetermined. In Figures 8 and 11, the capacity CDF curvesare shown for S1 and S2, respectively. As expected, at lowoutage, levels the capacity of the dual-polarized TX, dual-polarized RX antenna, (2, 2) and (2, 3) systems is about twicethat of the (1, 1) SISO system, and the difference between the(2, 2) and the (2, 3) systems is rather small. In order to as-sess the diversity performance, the envelope correlation [32]was determined between the received signals (latter being thecorrelation coefficient between the envelopes of the receivedsignals). Their CDFs are shown in Figures 9 and 12. As ex-pected, in Scenario 2, lower (even negative) correlation is tobe expected. Additionally, the relative received signal powerfor the (1, 1), (2, 2), and (2, 3) systems and their CDF was alsodetermined, which results are shown in Figures 10 and 13for the scenarios in consideration. Note that the confidencefor very low-probability (less than 0.01 or so) portions of thecurve might be low due to the relatively low number (about2000) of observations, but still validates the claim based onthe higher probability portion of the curves.

5. CONCLUSIONS

The main statement of this paper is that the generalizedcoded form of polarization diversity is a very good—maybethe best—way to apply the MIMO concept in multipathsatellite links. Two main contributions are related to themodeling of the conventional (2D) polarization diversitychannel and to the investigation via simulation of the 3DMIMO channel, respectively. (The relevant signal processingis called here PTC.)

Concerning the first of these (modeling), a physical sta-tistical model is given for the urban and the highway satellitemobile channels. Besides giving a validated model, it veri-fies once again the authors’ conviction that the best type of amultipath channel model is of the physical-statistical type.

Concerning the second of these (simulation), a very ex-tensive simulation study is carried out about the 3D polar-ization characteristics of the satellite multipath channel. Asynthetic satellite-to-indoor link is simulated and PTC char-

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Pro

babi

lity

(CE

P<

absc

issa

)

0 2 4 6 8 10 12 14 16 18 20

Capacity (bits/s/Hz)

nT = 1; nR = 1nT = 2; nR = 2nT = 2; nR = 3

Figure 8: CDF of the equal-power capacity (Scenario 1).

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Pro

babi

lity

(ρe<

absc

issa

)

−0.2 0 0.2 0.4 0.6 0.8 1

Envelope correlation

ρHy

ρHz

ρVy

ρVx

Figure 9: CDF of the envelope correlation (Scenario 1).

acteristics are investigated. The main purpose of this studywas to verify (for this example) the findings of two of theseauthors [15] about the capacity and diversity characteristicsof this type of channels. Results of this simulation are as fol-lows.

From the capacity point of view, (i) the difference be-tween the 2× 2 and the 2× 3 cases is negligible (as stated in[15]); and (ii) with high probability capacity of the MIMO,the situation is nearly exactly 2-times as high as that of theSISO case, again in accordance with [15]. (Note that with lowprobability, this difference is higher.)


10−3

10−2

10−1

100

Pro

babi

lity

(Pr<

absc

issa

)

−50 −45 −40 −35 −30 −25 −20 −15 −10

Combined received power (dBm)

nT = 1; nR = 1nT = 2; nR = 2nT = 2; nR = 3

Figure 10: CDF of the received power (Scenario 1).

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Pro

babi

lity

(CE

P<

absc

issa

)

0 2 4 6 8 10 12 14 16 18

Capacity (bits/s/Hz)

nT = 1; nR = 1nT = 2; nR = 2nT = 2; nR = 3

Figure 11: CDF of the equal-power capacity (Scenario 2).

To characterize the diversity performance, CDF of the re-ceived power in the various situations is investigated; resultshows that 3-fold (i.e., 3D) polarization diversity yields sig-nificantly higher received power than the 2-fold diversity (orthe nondiversity case).

From the simulation point of view, this study shows thatthe FDTD method is very well applicable to investigate in anexact way such extremely complex structures as the one here.A statement of this paper (stated but not discussed in detail)talking about satellite-diversity-MIMO, the problems briefly

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Pro

babi

lity

(ρe<

absc

issa

)

−0.2 0 0.2 0.4 0.6 0.8 1

Envelope correlation

ρHy

ρHz

ρVy

ρVx

Figure 12: CDF of the envelope correlation (Scenario 2).

10−3

10−2

10−1

100

Pro

babi

lity

(Pr<

absc

issa

)

−50 −45 −40 −35 −30 −25 −20 −15 −10

Combined received power (dBm)

nT = 1; nR = 1nT = 2; nR = 2nT = 2; nR = 3

Figure 13: CDF of the received power (Scenario 2).

dealt with in Section 3, that is, the effect of extremely largeand variable difference between the path-lengths of MIMObranches must be taken into account.

ACKNOWLEDGMENTS

This work was done in the framework of and is supported bythe project SatNEx of the EU IST FP6 Program. Their sup-port is gratefully acknowledged.


REFERENCES

[1] Z. Bodnar, Z. Herczku, J. Berces, et al., “A detailed experimen-tal study of the LEO satellite to indoor channel characteristics,”International Journal of Wireless Information Networks, vol. 6,no. 2, pp. 79–91, 1999.

[2] P. R. King, B. G. Evans, and S. Stavrou, “Physical-statisticalmodel for the land mobile-satellite channel applied to satel-lite/HAP MIMO,” in Proceedings of the 11th European WirelessConference, vol. 1, pp. 198–204, Nicosia, Cyprus, April 2005.

[3] T. Hult and A. Mohammed, “MIMO antenna applications forLEO satellite communications,” in Proceedings of the 3rd ESAInternational Workshop of the European COST 280, Prague,Czech Republic, June 2005.

[4] F. Yamashita, K. Kobayashi, M. Ueba, and M. Umehira,“Broadband multiple satellite MIMO system,” in Proceedingsof the 62nd IEEE Vehicular Technology Conference (VTC ’05),vol. 4, pp. 2632–2636, Dallas, Tex, USA, September 2005.

[5] K. Liolis, A. Panagopoulos, and P. Cottis, “Outage capacitystatistics of MIMO satellite networks operating at Ka band andabove,” in Proceedings of the 12th Ka and Broadband Commu-nications Conference, Naples, Italy, September 2006.

[6] J. Mietzner and P. A. Hoeher, “Distributed space-time codesfor cooperative wireless networks in the presence of differentpropagation delays and path losses,” in Proceedings of the IEEESensor Array and Multichannel Signal Processing Workshop, pp.264–268, Barcelona, Spain, July 2004.

[7] J. N. Laneman and G. W. Wornell, “Distributed space-time-coded protocols for exploiting cooperative diversity in wirelessnetworks,” IEEE Transactions on Information Theory, vol. 49,no. 10, pp. 2415–2425, 2003.

[8] M. Janani, A. Hedayat, T. E. Hunter, and A. Nosratinia,“Coded cooperation in wireless communications: space-timetransmission and iterative decoding,” IEEE Transactions onSignal Processing, vol. 52, no. 2, pp. 362–371, 2004.

[9] A. Sendonaris, E. Erkip, and B. Aazhang, “User cooperationdiversity—part I: system description,” IEEE Transactions onCommunications, vol. 51, no. 11, pp. 1927–1938, 2003.

[10] A. Sendonaris, E. Erkip, and B. Aazhang, “User cooper-ation diversity—part II: implementation aspects and per-formance analysis,” IEEE Transactions on Communications,vol. 51, no. 11, pp. 1939–1948, 2003.

[11] H. T. Cheng, H. Mheidat, M. Uysal, and T. M. Lok, “Dis-tributed space-time block coding with imperfect channel esti-mation,” in Proceedings of the IEEE International Conference onCommunications (ICC ’05), vol. 1, pp. 583–587, Seoul, SouthKorea, May 2005.

[12] T. Svantesson, M. A. Jensen, and J. W. Wallace, “Analysis ofelectromagnetic field polarizations in multiantenna systems,”IEEE Transactions on Wireless Communications, vol. 3, no. 2,pp. 641–646, 2004.

[13] B. N. Getu and J. B. Andersen, “The MIMO cube—a compactMIMO antenna,” IEEE Transactions on Wireless Communica-tions, vol. 4, no. 3, pp. 1136–1141, 2005.

[14] L. Dong, H. Choo, R. W. Heath Jr., and H. Ling, “Simulation ofMIMO channel capacity with antenna polarization diversity,”IEEE Transactions on Wireless Communications, vol. 4, no. 4,pp. 1869–1873, 2005.

[15] P. Horvath and I. Frigyes, “Application of the 3D polariza-tion concept in satellite MIMO systems,” in Proceedings ofthe 49th Annual IEEE Global Telecommunications Conference(GLOBECOM ’06), San Francisco, Calif, USA, November-December 2006.

[16] P. Horvath and I. Frigyes, “Investigation of the polarizationproperties of satellite channels with multiple antennas,” inProceedings of the 1st European Conference on Antennas andPropagation (EuCAP ’06), Nice, France, November 2006.

[17] P. Elia and P. Kumar, “Constructions of cooperative diversityschemes for asynchronous wireless networks,” in Proceedingsof IEEE International Symposium on Information Theory, pp.2724–2728, Seattle, Wash, USA, July 2006.

[18] S. Wei, D. L. Goeckel, and M. C. Valenti, “Asynchronous co-operative diversity,” IEEE Transactions on Wireless Communi-cations, vol. 5, no. 6, pp. 1547–1557, 2006.

[19] I. Frigyes and P. Horvath, “Polarization-time coding in satellitelinks,” IEEE Satellite and Space Newsletter, vol. 15, no. 2, pp. 6–8, 2005.

[20] S. M. Alamouti, “A simple transmit diversity technique forwireless communications,” IEEE Journal on Selected Areas inCommunications, vol. 16, no. 8, pp. 1451–1458, 1998.

[21] I. Frigyes, B. G. Molnar, Z. Herczku, and Z. Bodnar, “Antennagain and polarization effects in wireless links—accent on LEOsatellites,” Space Communications, vol. 19, no. 3-4, pp. 199–208, 2004.

[22] I. H. Cavdar, H. Dincer, and K. Erdogdu, “Propagation mea-surements at L-band for land mobile satellite link design,” inProceedings of the 7th Mediterranean Electrotechnical Confer-ence (MELECON ’94), vol. 3, pp. 1162–1165, Antalya, Turkey,April 1994.

[23] P. R. King and S. Stavrou, “Low elevation wideband land mo-bile satellite MIMO channel characteristics,” to appear in IEEETransactions on Wireless Communications.

[24] P. R. King and S. Stavrou, “Capacity improvement for a landmobile single satellite MIMO system,” IEEE Antennas andWireless Propagation Letters, vol. 5, no. 1, pp. 98–100, 2006.

[25] M. Born and E. Wolf, Principles of Optics, Cambridge Univer-sity Press, Cambridge, UK, 1998.

[26] D. Han, Y. S. Kim, and M. E. Noz, “Stokes parameters as aMinkowskian four-vector,” Physical Review E, vol. 56, no. 5,pp. 6065–6076, 1997.

[27] M. R. Andrews, P. P. Mitra, and R. de Carvalho, “Tripling thecapacity of wireless communications using electromagneticpolarization,” Nature, vol. 409, no. 6818, pp. 316–318, 2001.

[28] J. J. Gil, J. M. Correas, P. A. Melero, and C. Ferreira, “Gen-eralized polarization algebra,” http://www.unizar.es/galdeano/actas pau/PDFVIII/pp161-167.pdf.

[29] T. L. Marzetta, “Fundamental limitations on the capacity ofwireless links that use polarimetric antenna arrays,” in Pro-ceedings of IEEE International Symposium on Information The-ory, p. 51, Lausanne, Switzerland, June-July 2002.

[30] A. Taflove and S. C. Hagness, Computational Electrodynamics:The Finite-Difference-Time-Domain Method, Artech House,Norwood, Mass, USA, 2006.

[31] D. Gesbert, M. Shafi, D.-S. Shiu, P. J. Smith, and A. Naguib,“From theory to practice: an overview of MIMO space-timecoded wireless systems,” IEEE Journal on Selected Areas inCommunications, vol. 21, no. 3, pp. 281–302, 2003.

[32] R. G. Vaughan and J. B. Andersen, “Antenna diversity in mo-bile communications,” IEEE Transactions on Vehicular Tech-nology, vol. 36, no. 4, pp. 149–172, 1987.


Research ArticlePerformance Analysis of SSC Diversity Receivers overCorrelated Ricean Fading Satellite Channels

Petros S. Bithas and P. Takis Mathiopoulos

Institute for Space Applications and Remote Sensing, National Observatory of Athens, Metaxa and Vas. Pavlou Street,15236 Athens, Greece

Received 3 October 2006; Revised 23 February 2007; Accepted 6 April 2007


This paper studies the performance of switch and stay combining (SSC) diversity receivers operating over correlated Ricean fadingsatellite channels. Using an infinite series representation for the bivariate Ricean probability density function (PDF), the PDF ofthe SSC output signal-to-noise ratio (SNR) is derived. Capitalizing on this PDF, analytical expressions for the corresponding cu-mulative distribution function (CDF), the moments of the output SNR, the moments generating function (MGF), and the averagechannel capacity (CC) are derived. Furthermore, by considering several families of modulated signals, analytical expressions forthe average symbol error probability (ASEP) for the diversity receivers under consideration are obtained. The theoretical analy-sis is accompanied by representative performance evaluation results, including average output SNR (ASNR), amount of fading(AoF), outage probability (Pout), average bit error probability (ABEP), and average CC, which have been obtained by numericaltechniques. The validity of some of these performance evaluation results has been verified by comparing them with previouslyknown results obtained for uncorrelated Ricean fading channels.

Copyright © 2007 P. S. Bithas and P. T. Mathiopoulos. This is an open access article distributed under the Creative CommonsAttribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work isproperly cited.

1. INTRODUCTION

The mobile terrestrial and satellite communication channelis particularly dynamic due to multipath fading propaga-tion, having a strong negative impact on the average bit er-ror probability (ABEP) of any modulation scheme [1]. Di-versity is a powerful communication receiver technique usedto compensate for fading channel impairments. The mostimportant and widely used diversity reception methods em-ployed in digital communication receivers are maximal-ratiocombining (MRC), equal-gain combining (EGC), selectioncombining (SC), and switch and stay combining (SSC) [2].For SSC diversity considered in this paper, the receiver se-lects a particular branch until its signal-to-noise ratio (SNR)drops below a predetermined threshold. When this happens,the combiner switches to another branch and stays there re-gardless of whether the SNR of that branch is above or be-low the predetermined threshold. Hence, among the above-mentioned diversity schemes, SSC is the least complex andcan be used in conjunction with coherent, noncoherent, anddifferentially coherent modulation schemes. It is also wellknown that in many real life communication scenarios the

combined signals are correlated [2, 3]. A typical example forsuch signal correlation exists in relatively small-size mobileterminals where typically the distance between the diversityantennas is short. Due to this correlation between the signalsreceived at the diversity branches there is a degradation in theachievable diversity gain.

The Ricean fading distribution is often used to modelpropagation paths consisting of one strong direct line-of-sight (LoS) signal and many randomly reflected and usuallyweaker signals. Such fading environments are typically en-countered in microcellular and mobile satellite radio links[2]. In particular for mobile satellite communications theRicean distribution is used to accurately model the mo-bile satellite channel for single- [4] and clear-state [5] chan-nel conditions. Furthermore, in [6] it was depicted that theRicean K-factor characterizes the land mobile satellite chan-nel during unshadowed periods.

The technical literature concerning diversity receivers op-erating over correlated fading channels is quite rich, for ex-ample, see [7–13]. In [7] expressions for the outage probabil-ity (Pout) and the ABEP of dual SC with correlated Rayleighfading were derived either in closed form or in terms of


single integrals. In [8] the cumulative distribution functions(CDF) of SC, in correlated Rayleigh, Ricean, and Nakagami-m fading channels were derived in terms of single-fold in-tegrals and infinite series expressions. In [9] the ABEP ofdual-branch EGC and MRC receivers operating over corre-lated Weibull fading channels was obtained. In [10] the per-formance of MRC in nonidentical correlated Weibull fad-ing channels with arbitrary parameters was evaluated. In[11] an analysis for the Shannon channel capacity (CC) ofdual-branch SC diversity receivers operating over correlatedWeibull fading was presented. In [12], infinite series expres-sions for the capacity of dual-branch MRC, EGC, SC, andSSC diversity receivers over Nakagami-m fading channelshave been derived.

Past work concerning the performance of SSC operat-ing over correlated fading channels can be found in [14–17]. One of the first attempts to investigate the performanceof SSC diversity receivers operating over independent andcorrelated identical distributed Ricean fading channels wasmade in [14]. However, in this reference only noncoher-ent frequency shift keying (NCFSK) modulation was con-sidered and its ABEP has been derived in an integral rep-resentation form. In [15] the performance of SSC diversityreceivers was investigated for different fading channels, in-cluding Rayleigh, Nakagami-m and Ricean, and under dif-ferent channel conditions but dealt mainly with uncorre-lated fading. For correlated fading in this reference only theNakagami-m distribution was studied. In [16] the momentsgenerating function (MGF) of SSC was presented in terms ofa finite integral representation for the correlated Nakagami-m fading channel. In [17] expressions for the average outputSNR (ASNR), amount of fading (AoF) and Pout for the cor-related log-normal fading channels have been derived.

All in all, the problem of theoretically analyzing the per-formance of SSC over correlated Ricean fading channels hasnot yet been thoroughly addressed in the open technical lit-erature. The main difficulty in analyzing the performance ofdiversity receivers in correlated Ricean fading channels is thecomplicated form of the received signal bivariate probabilitydensity function (PDF), see [14, Equation (17)], and the ab-sence of an alternative and more convenient expression forthe multivariate distribution. An efficient solution to thesedifficulties is to employ an infinite series representation forthe bivariate PDF, such as those that were proposed in [18]or [19]. Such an approach was used in [20] to analyze the per-formance of MRC, EGC, and SC in the presence of correlatedRicean fading. Similarly here the most important statisticalmetrics and the capacity of SSC diversity receivers operat-ing over correlated Ricean fading channels will be studied. Inparticular, we derive the PDF, CDF, MGF, moments and theaverage CC of such receivers operating over correlated Riceanfading channels. Furthermore, analytical expressions for theaverage symbol error probability (ASEP) of several modula-tion schemes will be obtained. Capitalizing on these expres-sions, a detailed performance analysis for the Pout, ASNR,AoF, and ASEP/ABEP will be presented.

The remainder of this paper is organized as follows. Af-ter this introduction, in Section 2 the system model is intro-

duced. In Section 3, the SSC received signal statistics are pre-sented, while in Section 4 the capacity is obtained. Section 5contains the derivation of the most important performancemetrics of the SSC output SNR. In Section 6, various numer-ical evaluation results are presented and discussed, while theconclusions of the paper can be found in Section 7.

2. SYSTEM MODEL

By considering a dual-branch SSC diversity receiver operat-ing over a correlated Ricean fading channel, the baseband re-ceived signal at the �th (� = 1 and 2) input branch can bemathematically expressed as

ζ� = sh� + n�. (1)

In the above equation, s is the transmitted complex sym-bol, h� is the Ricean fading channel complex envelope withmagnitude R� = |h�|, and n� is the additive white Gaus-sian noise (AWGN) having single-sided power spectral den-sity of N0. The usual assumption for ideal fading phase esti-mation is made, and hence, only the distributed fading enve-lope and the AWGN affect the received signal. Moreover, theAWGN is assumed to be uncorrelated between the two diver-sity branches. The instantaneous SNR per symbol at the �thinput branch is γ� = R2

�Es/(2N0), where Es = E〈|s|2〉 is thetransmitted average symbol energy, where E〈·〉 denoting ex-pectation and | · | absolute value. The corresponding averageSNR per symbol at both input branches is γ = ΩEs/N0, whereΩ = E〈R2

�〉. The PDF of the SNR of the Ricean distributionis given by [2, Equation (2.16)]

fγ(γ) = 1 + K

γexp

[− K − (1 + K)

γγ]

× I0[

2

√K(K + 1)

γγ1/2

],

(2)

where K is the Ricean K-factor defined as the power ratioof the specular signal to the scattered signals and I0(·) is thezeroth-order modified Bessel function of the first kind [21,Equation (8.406)]. The CDF of γ is given by [14, Equation(8)]

Fγ(γ) = Q1

[√2K ,

√2(1 + K)

γγ

], (3)

where Q1(·) is the first-order Marcum-Q function [2, Equa-tion (4.33)].

The joint PDF of γ1 and γ2, presented in [14, Equation(17)], can be expressed in terms of infinite series by follow-ing a similar procedure as for deriving [18, Equation (9)].Hence, substituting I0(·) with its infinite series representa-tion [21, Equation (8.445)], expanding the term [γ1 + γ2 +2√γ1γ2 cos(θ)]i using the multinomial identity [22, Equa-tion (24.1.2)], using [21, Equation (3.389/1)] and after some

P. S. Bithas and P. T. Mathiopoulos 3

mathematical manipulations the joint PDF of γ1, γ2 can beexpressed as

fγ1,γ2

(γ1, γ2

) =∞∑

i,h=0v1+v2+v3=i

A exp[− β1

(γ1 + γ2

)]

× (Bγ

β2−11 γ

β3−12 + Cγ−1γ

β2−1/21 γ

β3−1/22

)(4)

with

A = 2v3+2h−1(1 + K)1+β4ρ2hKi exp[− 2K/(1 + ρ)

]√πγ1+β4

(1− ρ2

)1+2hv1!v2!v3!i!(1 + ρ)2i

,

B =[1 + (−1)v3

]Γ[h +

(1 + v3

)/2]

Γ(h + 1 + v3/2

)Γ(1 + 2h

) ,

C =[− 1 + (−1)v3

]2ρ(1 + K)Γ

(1 + h + v3/2

)(ρ2 − 1

)Γ(2 + 2h)Γ

[h +

(3 + v3

)/2] ,

β1 = (1 + K)(1− ρ2

)γ

, β2 = v1 +v3

2+ h + 1,

β3 = v2 +v3

2+ h + 1, β4 = i + 2h + 1,

(5)

where Γ(·) is the Gamma function [21, Equation (8.310/1)]and ρ is the correlation coefficient between γ1 and γ2. It canbe proved that the above infinite series expression alwaysconverges [18].

3. RECEIVED SIGNAL STATISTICS

In this section, the most important statistical metrics,namely, the PDF, CDF, MGF, and moments of dual branchSSC output SNR diversity receivers operating over correlatedRicean fading channels will be presented.

3.1. Probability density function (PDF)

Let γssc be the instantaneous SNR per symbol at the output ofthe SSC and γτ the predetermined switching threshold. Fol-lowing [15], the PDF of γssc, fγssc (γ), is given by

fγssc (γ) =⎧⎪⎨⎪⎩rssc(γ), γ ≤ γτ ,

rssc(γ) + fγ(γ), γ > γτ.(6)

Moreover, rssc(γ) is given in [23, Equation (21b)] as

rssc(γ) =∫ γτ

0fγ1γ2

(γ, γ2

)dγ2

=∫∞

0fγ1γ2

(γ, γ2

)dγ2 −

∫∞γτfγ1γ2

(γ, γ2

)dγ2.

(7)

Hence, by substituting (4) in (7) and using [21, Equation(3.351/2-3)], these integrals can be solved and rssc(γ) can beexpressed as

rssc(γ) =∞∑

i,h=0v1+v2+v3=i

A exp(− β1γ

)γβ2−1/2

×[

Bγ(β3,β1γτ

)√γβ

β3

1

+Cγ

(β3 + 1/2,β1γτ

)γβ

β3+1/21

],

(8)

where γ(·, ·) is the lower incomplete Gamma function [21,Equation (8.350/1)].

3.2. Cumulative distribution function (CDF)

Similar to [23, Equation (20)], the CDF of γssc, Fγssc (γ), isgiven by

Fγssc (γ) = Pr(γτ ≤ γ1 ≤ γ

)+ Pr

(γ2 < γτ ∧ γ1 < γ

)(9)

which after some manipulations can be expressed in terms ofCDFs as

Fγssc (γ) =⎧⎪⎨⎪⎩Fγ1,γ2

(γ, γτ

), γ ≤ γτ ,

Fγ(γ)− Fγ(γτ)

+ Fγ1,γ2

(γ, γτ

), γ > γτ.

(10)

Hence, by substituting (4) in Fγ1,γ2 (γ, γτ) = ∫ γ0

∫ γτ0 fγ1,γ2 (γ1,

γ2)dγ1dγ2 using [21, Equation (3.351/1)], Fγ1,γ2 (γ, γτ) can bederived as

Fγ1,γ2

(γ, γτ

) =∞∑

i,h=0v1+v2+v3=i

A

ββ2+β3

1

×[Bγ

(β2,β1γ

)γ(β3,β1γτ

)

+Cβ1γ

γ(β2 +

12

,β1γ)γ(β3 +

12

,β1γτ

)].

(11)

In order to verify the validity of the above derivations,(10) and (11) have been numerically evaluated for the spe-cial case of uncorrelated, that is, ρ = 0, Ricean fading chan-nels. The resulting CDF was found to be identical to the sameCDF presented in [2, Equation 9.273], which was derived us-ing a different mathematical approach as a closed-form ex-pression.

3.3. Moments generating function (MGF)

Based on (6), the MGF of γssc, Mγssc (s) = E〈exp(−sγssc)〉, [24,Equation (5.62)], can be expressed in terms of two integralsas

Mγssc (s) =∫∞

0exp(−sγ)rssc(γ)dγ

+∫∞γτ

exp(−sγ) fγ(γ)dγ = I1 + I2.

(12)


Using [21, Equation (3.381/4)], I1 can be expressed in termsof infinite series as

I1 =∞∑

i,h=0v1+v2+v3=i

A

[Γ(β2)

(β1 + s

)β2Bβ

−β3

1 γ(β3,β1γτ

)

+Cβ−β3−1/21

Γ(β2 +1/2

)(β1 +s

)β2+1/2 γ(β3+

12

,β1γτ)].

(13)

Setting ψ =√

2γ[(1 + K)/γ + s] and using [2, Equation(4.33)], I2 can be solved as

I2 = Q1

[√2K(1 + K)1 + K + γs

,

√√√2(1 + K + γ s)γτγ

]

× exp[K(1 + K)1 + K + sγ

](1 + K) exp(−K)

1 + K + γs.

(14)

3.4. Moments

Based on (6), the moments for γssc, μγssc (n) = E〈exp(γnssc)〉,[24, Equation (5.38)], can be expressed in terms of two inte-grals as

μγssc (n) =∫∞

0γnrssc(γ)dγ +

∫∞γτγn fγ(γ)dγ

= I3 + I4.

(15)

Using again [21, Equation (3.381/4)], I3 can be expressed interms of infinite series as

I3 =∞∑

i,h=0v1+v2+v3=i

A[Bγ

(β3,β1γτ

)Γ(n + β2)

ββ2+β3+n1

+Cγ

(β3 + 1/2,β1γτ

)ββ2+β3+n+11

Γ(n + β2 +

12

)].

(16)

Setting φ =√

2γ(1 + K)/γ in I4, using [2, Equation(4.104)], after some straight-forward mathematical manip-ulations, yields

I4 = γn−1

2n(1 + K)n−1Q2n+1,0

(K ,

√√√2(1 + K)γτγ

), (17)

where Qm,n(·, ·) is the Nuttal Q-function defined in [25].

4. CHANNEL CAPACITY (CC)

CC is a well-known performance metric providing an upperbound for maximum errorless transmission rate in a Gaus-sian environment. The average CC, C, is defined as [26]

CΔ= BW

∫∞0

log2(1 + γ) fγssc (γ)dγ, (18)

where BW is transmission bandwidth of the signal in Hz.Hence, substituting (6) in (18), C becomes

C =∫∞

0log2(1 + γ)rssc(γ)dγ +

∫∞γτ

log2(1 + γ) fγ(γ)dγ

= I5 + I6.

(19)

By representing ln(1 + γ) = G1,22,2

[γ | 1,1

1,0

], [27, Equation

(01.04.26.0003.01)], and exp(−γ) = G1,00,1

[γ | 0−

], [27, Equa-

tion (01.03.26.0004.01)], where G(·) is Meijer’s G-function[21, Equation (9.301)] and using [28], I5 can be solved as

I5 =∞∑

i,h=0v1+v2+v3=i

A

ln 2

{Bγ(β3,β1γτ

)ββ3+β2

1

G1,33,2

[1β1

∣∣∣∣ 1, 1, 1− β2

1, 0

]

+ Cγ(β3 + 1/2,β1γτ

)ββ3+β2+3/21

×G1,33,2

[1β1

∣∣∣∣ 1, 1, 1− β2

1, 0

]}.

(20)

Due to the very complicated nature of I6, it is very difficult,if not impossible, to derive a closed-form solution for thisintegral. However, I6 can be evaluated via numerical inte-gration using any of the well-known mathematical softwarepackages, such as MATHEMATICA or MATLAB.

5. PERFORMANCE ANALYSIS

In this section a detailed performance analysis, in terms ofPout, ASEP, ASNR and AoF, for SSC diversity receivers operat-ing over correlated Ricean fading channels will be presented.

5.1. Outage probability (Pout)

Pout is the probability that the output SNR falls below a pre-determined threshold γth, Pout(γth), and can be obtained byreplacing γ with γth in (10) as

Pout(γth

) = Fγssc

(γth

). (21)

5.2. Average symbol error probability (ASEP)

The ASEP, Pse, can be evaluated directly by averaging the con-ditional symbol error probability, Pe(γ), over the PDF of γssc

[29]

Pse =∫∞

0Pe(γ) fγssc (γ)dγ. (22)

For different families of modulation schemes, Pe(γ) canbe obtained as follows.

(i) For binary phase shift keying (BPSK) and square M-ary quadrature amplitude modulation (QAM) signaling for-

mats and for high-input SNR, Pe(γ) = D erfc(√Eγ), where


erfc(·) is the complementary error function [21, Equation(8.250/1)] and D, E are constants the values of which dependon the specific modulation scheme under consideration. Us-ing this expression, by substituting (6) in (22), yields

Pse =∫∞

0D erfc

(√Eγ

)rssc(γ)dγ +

∫∞γτD erfc

(√Eγ

)fγ(γ)dγ

= I7 + I8.(23)

Expressing erfc(√Eγ) = √

π−1G2,01,2

[Bγ | 1

0,1/2

], [27, Equation

(06.27.26.0006.01)], and exp(−γ) = G1,00,1

[γ | 0−

], [27, Equa-

tion (01.03.26.0004.01)], using [28] and after some straight-forward mathematical manipulations I7 can be expressed as

I7 =∞∑

i,h=0v1+v2+v3=i

ADΓ(β2 + 1/2

)√πβ

β3

1 Eβ2

×{

BΓ(β2)

Γ(β2 + 1

)γ(β3,β1γτ)

× 2F1

(β2,β2 +

12

;β2 + 1;−β1

E

)

+Cγ

(β3 + 1/2,β1γτ

)Γ(β2 + 1

)(β1E

)1/2Γ(β2 +

32

)

× 2F1

(β2 +

12

,β2 + 1;β2 +32

;−β1

E

)}

(24)

with 2F1(·, ·; ·; ·) being Gauss Hypergeometric function [21,

Equation (9.100)]. Moreover, I8 =∫∞

0 D erfc(√Eγ) fγ(γ)dγ−∫ γτ

0 D erfc(√Eγ) fγ(γ)dγ = I8,a − I8,b. Hence, substituting

again I0(·) with its infinite series representation [21, Equa-tion (8.445)], I8,a can be solved with the aid of [28] and I8,b

using [27, Equation (06.27.21.0019.01)]. Thus, using thesesolutions of I8,a and I8,b and after some mathematical ma-nipulations, I8 can be expressed as in (25):

I8 = D(1 + K) exp(−K)γ

∞∑k=0

(k!)−2[K(K + 1)

γ

]k

×{Γ(k + 1)Γ(k + 3/2)√

πEk+1Γ(k + 2)

× 2F1

[k + 1, k +

32

; k + 2;−1 + K

γE

]

− 2√E/π[

β1(1− ρ2

)]k+3/2

∞∑ρ=0

[− (1 + K)/γ]ρEρ

(2ρ + 1)ρ!

×Γ[k+

32

+ρ,(1+K)γτ

γ

]− Γ

[k+1, (1+K)γτ/γ

]2[β1(1−ρ2

)]k+1

}.

(25)

In (25), Γ(·, ·) is the upper incomplete Gamma function [22,Equation (6.51)].

(ii) For noncoherent binary frequency shift keying(BFSK) and binary differential phase shift keying (BDPSK),Pe(γ) = D exp(−Dγ). Similar to the derivation of (12), thatis, using [21, Equation (3.381/4)] and [2, Equation (4.33)],Pse can be expressed as

Pse =∞∑

i,h=0v1+v2+v3=i

AD

×[

Γ(β2)B(

β1 + E)β2β

β3

1

γ(β3,β1γτ

)

+CΓ

(β2 + 1/2

)(β1 + E

)β2+1/2ββ3+1/21

γ(β3 +

12

,β1γτ

)]

+Q1

[√2K(1 + K)1 + K + γE

,

√√√2(1 + K + γE)γτγ

]

× exp[K(1 + K)

1 + K + γE

](1 + K) exp(−K)

1 + K + γE.

(26)

(iii) For Gray encoded M-ary PSK and M-ary DPSK,Pe(γ) = D

∫ Λ0 exp[−E(θ)γ]dθ, where Λ is constant. Thus, Pse

can be expressed as

Pse =∞∑

i,h=0v1+v2+v3=i

AD

×{

Bγ(β3,β1γτ

)ββ3

1

∫ Λ

0

Γ(β2)

[β1 + E(θ)

]β2dθ

+Cγ

(β3 + 1/2,β1γτ

)ββ3+1/21

×∫ Λ

0

Γ(β2 + 1/2)[

β1 + E(θ)]β2+1/2 dθ

}

+∫ Λ

0Q1

[√2K(1 + K)

g(θ),

√√√2g(θ)γτγ

]

× exp[K(1 + K)g(θ)

](1 + K) exp(−K)

g(θ)dθ,

(27)

where g(θ) = 1 +K +γE(θ). The above finite integrals can beeasily evaluated via numerical integration.

5.3. Average output SNR (ASNR) andamount of fading (AoF)

The ASNR, γssc, is a useful performance measure serving asan excellent indicator for the overall system fidelity and canbe obtained from the first-order moment of γssc as

γssc = μγssc (1). (28)


1

1.05

1.1

1.15

1.2

1.25

1.3

Nor

mal

ized

aver

age

outp

ut

SNR

1 2 3 4 5 6 7 8 9

Ricean K-Factor

ρ = 0.1ρ = 0.3ρ = 0.5

ρ = 0.7ρ = 0.9

Figure 1: Normalized average output SNR (ASNR) versus theRicean K-factor for several values of the correlation coefficient ρ.

The AoF, defined as AoFΔ= var(γssc)/γ2

ssc, is a unified mea-sure of the severity of the fading channel [2] and gives aninsight to the performance of the entire system. It can be ex-pressed in terms of first- and second-order moments of γssc

as

AoF = μγssc (2)

μγssc (1)2− 1. (29)

6. PERFORMANCE EVALUATION RESULTS

Using the previous mathematical analysis, various perfor-mance evaluation results have been obtained by means ofnumerical techniques and will be presented in this section.Such results include performances for the ASNR, AoF, Pout,ABEP1, and C and will be presented for different Riceanchannel conditions, that is, different values for K and ρ, aswell as for various modulation schemes.

In Figures 1 and 2 the normalized ASNR (γssc/γ) and AoFare plotted as functions of the RiceanK-factor for several val-ues of the correlation coefficient ρ. These performance eval-uation results have been obtained by numerically evaluating(15)–(17), (28), and (29). The results presented in Figure 1

1 For the consistency of the presentation from now on instead of the ASEPthe ABEP performance will be used. As it is well known [2] for M-ary(M > 2) modulation schemes, assuming Gray encoding, the ABEP canbe simply obtained from the ASEP as Pbe ∼= Pse/ log2 M, since Es =Eb log2 M, where Eb denotes the transmitted average bit energy.

1 2 3 4 5 6 7 8

Ricean K-Factor

ρ = 0.1ρ = 0.3ρ = 0.5

ρ = 0.7ρ = 0.9

0.2

0.3

0.4

0.5

0.6

0.7

Am

oun

tof

fadi

ng

(AoF

)

Figure 2: Amount of fading (AoF) versus the Ricean K-factor forseveral values of the correlation coefficient ρ.

show that as K increases, that is, the severity of the fading de-creases, and/or ρ increases, the normalized ASNR decreases,resulting in a reduced diversity gain. We note that similar ob-servations have been made in [3, 30]. Furthermore, the re-sults presented in Figure 2 indicate that asK increases and/orρ decreases, AoF is degraded.

Next the ABEP has been obtained using (23)–(27). InFigures 3 and 4 the ABEP is plotted as a function of the av-erage input SNR per bit, that is, γb = γ/ log2 M, for severalvalues of K . Figure 3 considers the performance of DBPSK,BPSK, and M-ary PSK signaling formats and ρ = 0.5. Asexpected, when K increases, the ABEP improves and BPSKexhibits the best performance. Figure 4 presents the ABEPof 16-QAM for different values of ρ and K . For comparisonpurposes, the performance of an equivalent single receiver,that is, without diversity, is also included. Similar to the pre-vious cases, it is observed that the ABEP improves as K in-creases and/or ρ decreases, while significant overall perfor-mance improvement, as compared to the no-diversity case,is also noted.

In Figure 5, Pout is plotted as a function of the normalizedoutage threshold per bit, γth/γb, for several values of K andρ. These performance results have been obtained by numer-ically evaluating (10), (11), and (21) and for ρ = 0 they areidentical to the ones obtained by using [2, Equation 9.273].It is observed that Pout decreases, that is, the outage perfor-mance improves, as K increases and/or ρ decreases.

Finally, the normalized average CC can be obtained asC = C/BW (in b/s/Hz) by employing (19) and (20). InFigure 6, C is plotted as a function of γb for several values


10−4

10−3

10−2

10−1

Ave

rage

bit

erro

rpr

obab

ility

(AB

EP

)

DBPSKBPSK

8-PSK16-PSK

−5 0 5 10 15 20

Average input SNR per bit (dB)

K = 1

K = 8

Figure 3: Average bit error probability (ABEP) versus average in-put SNR per bit for DBPSK, BPSK, and M-PSK (M = 8 and 16)signaling formats, for different values of the Ricean K-factor.

10−5

10−4

10−3

10−2

10−1

Ave

rage

bit

erro

rpr

obab

ility

(AB

EP

)

K = 1K = 4K = 8

−5 0 5 10 15 20


ρ = 0.2

ρ = 0.6

No diversity

Figure 4: Average bit error probability (ABEP) versus average inputSNR per bit for 16-QAM signaling format for different values of theRicean K-factor and the correlation coefficient ρ.

10−4

10−3

10−2

10−1

1

Ou

tage

prob

abili

ty(P

out)

−10 −7.5 −5 −2.5 0 2.5 5

γth/γb

ρ = 0ρ = 0.4ρ = 0.8

K = 4

K = 8

K = 1

Figure 5: Outage probability (Pout) versus the normalized averageinput SNR per bit for several values of the Ricean K-factor and thecorrelation coefficient ρ.

0.5

1

1.5

2

2.5

3

−4 −2 0 2 4 6 8 10


Nor

mal

ized

aver

age

chan

nel

capa

city

(b/s

/Hz)

ρ = 0.1ρ = 0.4ρ = 0.7

ρ = 0.9

No diversity

Figure 6: Normalized average channel capacity (C/BW) versus theaverage input SNR per bit for several values of the correlation coef-ficient ρ.


of ρ and for K = 1. These results illustrate that as ρ increases,C decreases, as expected [12], and the receiver without diver-sity has always the worst performance.

7. CONCLUSIONS

In this paper, the performance of dual branch SSC diversityreceivers operating over correlated Ricean fading channelshas been studied. By deriving a convenient expression forthe bivariate Ricean PDF, analytical formulae for the mostimportant statistical metrics of the received signals and thecapacity of such receivers have been obtained. Capitalizingon these formulas, useful expressions for a number of per-formance criteria have been obtained, such as ABEP, Pout,ASNR, AoF, and average CC. Various performance evalua-tion results for different fading channel conditions have beenalso presented and compared with equivalent performanceresults of receivers without diversity.

ACKNOWLEDGMENTS

This work has been performed within the framework ofthe Satellite Network of Excellence (SatNEx-II) project (IST-027393), a Network of Excellence (NoE) funded by EuropeanCommission (EC) under the FP6 program.

REFERENCES

[1] T. S. Rappaport, Wireless Communications, Prentice-Hall PTR,Upper Saddle River, NJ, USA, 2002.

[2] M. K. Simon and M.-S. Alouini, Digital Communication overFading Channels, John Wiley & Sons, New York, NY, USA,2nd edition, 2005.

[3] N. C. Sagias and G. K. Karagiannidis, “Gaussian class mul-tivariate Weibull distributions: theory and applications infading channels,” IEEE Transactions on Information Theory,vol. 51, no. 10, pp. 3608–3619, 2005.

[4] G. E. Corazza and F. Vatalaro, “A statistical model for landmobile satellite channels and its application to nongeostation-ary orbit systems,” IEEE Transactions on Vehicular Technology,vol. 43, no. 3, part 2, pp. 738–742, 1994.

[5] H. Wakana, “A propagation model for land mobile satellitecommunications,” in Proceedings of IEEE Antennas and Propa-gation Society International Symposium, vol. 3, pp. 1526–1529,London, Ont, Canada, June 1991.

[6] E. Lutz, D. Cygan, M. Dippold, F. Dolainsky, and W. Papke,“The land mobile satellite communication channel-recording,statistics, and channel model,” IEEE Transactions on VehicularTechnology, vol. 40, no. 2, pp. 375–386, 1991.

[7] M. K. Simon and M.-S. Alouini, “A unified performance anal-ysis of digital communication with dual selective combin-ing diversity over correlated Rayleigh and Nakagami-m fad-ing channels,” IEEE Transactions on Communications, vol. 47,no. 1, pp. 33–43, 1999.

[8] Y. Chen and C. Tellambura, “Distribution functions of selec-tion combiner output in equally correlated Rayleigh, Rician,and Nakagami-m fading channels,” IEEE Transactions on Com-munications, vol. 52, no. 11, pp. 1948–1956, 2004.

[9] G. K. Karagiannidis, D. A. Zogas, N. C. Sagias, S. A. Kot-sopoulos, and G. S. Tombras, “Equal-gain and maximal-ratiocombining over nonidentical Weibull fading channels,” IEEE

Transactions on Wireless Communications, vol. 4, no. 3, pp.841–846, 2005.

[10] M. H. Ismail and M. M. Matalgah, “Performance of dualmaximal ratio combining diversity in nonidentical correlatedWeibull fading channels using Pade approximation,” IEEETransactions on Communications, vol. 54, no. 3, pp. 397–402,2006.

[11] N. C. Sagias, “Capacity of dual-branch selection diversity re-ceivers in correlative Weibull fading,” European Transactionson Telecommunications, vol. 17, no. 1, pp. 37–43, 2006.

[12] S. Khatalin and J. P. Fonseka, “Capacity of correlatedNakagami-m fading channels with diversity combining tech-niques,” IEEE Transactions on Vehicular Technology, vol. 55,no. 1, pp. 142–150, 2006.

[13] C.-D. Iskander and P. T. Mathiopoulos, “Performance ofdual-branch coherent equal-gain combining in correlatedNakagami-m fading,” Electronics Letters, vol. 39, no. 15, pp.1152–1154, 2003.

[14] A. A. Abu-Dayya and N. C. Beaulieu, “Switched diversity onmicrocellular Ricean channels,” IEEE Transactions on VehicularTechnology, vol. 43, no. 4, pp. 970–976, 1994.

[15] Y.-C. Ko, M.-S. Alouini, and M. K. Simon, “Analysis and opti-mization of switched diversity systems,” IEEE Transactions onVehicular Technology, vol. 49, no. 5, pp. 1813–1831, 2000.

[16] C. Tellambura, A. Annamalai, and V. K. Bhargava, “Unifiedanalysis of switched diversity systems in independent and cor-related fading channels,” IEEE Transactions on Communica-tions, vol. 49, no. 11, pp. 1955–1965, 2001.

[17] M.-S. Alouini and M. K. Simon, “Dual diversity over corre-lated log-normal fading channels,” IEEE Transactions on Com-munications, vol. 50, no. 12, pp. 1946–1959, 2002.

[18] D. A. Zogas and G. K. Karagiannidis, “Infinite-series repre-sentations associated with the bivariate Rician distributionand their applications,” IEEE Transactions on Communications,vol. 53, no. 11, pp. 1790–1794, 2005.

[19] M. K. Simon, Probability Distributions Involving GaussianRandom Variables: A Handbook for Engineers and Scientists,Kluwer Academic Publishers, Norwell, Mass, USA, 2002.

[20] P. S. Bithas, N. C. Sagias, and P. T. Mathiopoulos, “Dual diver-sity over correlated Ricean fading channels,” Journal of Com-munications and Networks, vol. 9, no. 1, pp. 67–74, 2007.

[21] I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series,and Products, Academic Press, New York, NY, USA, 6th edi-tion, 2000.

[22] M. Abramowitz and I. A. Stegun, Handbook of Mathemati-cal Functions with Formulas, Graphs and Mathematical Tables,Dover, New York, NY, USA, 9th edition, 1972.

[23] A. A. Abu-Dayya and N. C. Beaulieu, “Analysis of switched di-versity systems on generalized-fading channels,” IEEE Transac-tions on Communications, vol. 42, no. 11, pp. 2959–2966, 1994.

[24] A. Papoulis, Probability, Random Variables, and Stochastic Pro-cesses, McGraw-Hill, New York, NY, USA, 2nd edition, 1984.

[25] A. Nuttal, “Some integrals involving the Q-function,” Tech.Rep. 4297, Naval Underwater Systems Center, New London,Conn, USA, April 1972.

[26] W. C. Y. Lee, “Estimate of channel capacity in Rayleigh fad-ing environment,” IEEE Transactions on Vehicular Technology,vol. 39, no. 3, pp. 187–189, 1990.

[27] “The Wolfram functions site,” http://functions.wolfram.com/.[28] V. S. Adamchik and O. I. Marichev, “The algorithm for cal-

culating integrals of hypergeometric type functions and itsrealization in REDUCE system,” in Proceedings of Interna-tional Symposium on Symbolic and Algebraic Computation (IS-SAC ’90), pp. 212–224, Tokyo, Japan, August 1990.


[29] N. C. Sagias, D. A. Zogas, and G. K. Karagiannidis, “Selectiondiversity receivers over nonidentical Weibull fading channels,”IEEE Transactions on Vehicular Technology, vol. 54, no. 6, pp.2146–2151, 2005.

[30] P. S. Bithas, G. K. Karagiannidis, N. C. Sagias, P. T. Mathiopou-los, S. A. Kotsopoulos, and G. E. Corazza, “Performance analy-sis of a class of GSC receivers over nonidentical Weibull fadingchannels,” IEEE Transactions on Vehicular Technology, vol. 54,no. 6, pp. 1963–1970, 2005.


Research ArticleAdvanced Fade Countermeasures for DVB-S2 Systems inRailway Scenarios

Stefano Cioni,1 Cristina Parraga Niebla,2 Gonzalo Seco Granados,3 Sandro Scalise,2

Alessandro Vanelli-Coralli,1 and Marıa Angeles Vazquez Castro3

1 ARCES, University of Bologna, Via Toffano 2, 40125 Bologna, Italy2 German Aerospace Center (DLR), Institute of Communications and Navigation, Postfach 1116, 82230 Wessling, Germany3 Department of Telecommunications and Systems Engineering, Universitat Autonoma de Barcelona, Campus Universitari, s/n,08193 Bellatera, Barcelona, Spain

Received 22 October 2006; Accepted 3 June 2007


This paper deals with the analysis of advanced fade countermeasures for supporting DVB-S2 reception by mobile terminalsmounted on high-speed trains. Recent market studies indicate this as a potential profitable market for satellite communications,provided that integration with wireless terrestrial networks can be implemented to bridge the satellite connectivity inside railwaytunnels and large train stations. In turn, the satellite can typically offer the coverage of around 80% of the railway path with existingspace infrastructure. This piece of work, representing the first step of a wider study, is focusing on the modifications which maybe required in the DVB-S2 standard (to be employed in the forward link) in order to achieve reliable reception in a challengingenvironment such as the railway one. Modifications have been devised trying to minimize the impact on the existing air interface,standardized for fixed terminals.

Copyright © 2007 Stefano Cioni et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1. INTRODUCTION

Satellite communications developed to a tremendous globalsuccess in the field of analog and then digital audio/TVbroadcasting by exploiting the inherent wide-area coveragefor the distribution of content. It appeared a “natural” con-sequence to extend the satellite services for point-to-pointmultimedia applications, by taking advantage of the ability ofsatellite to efficiently distribute multimedia information oververy large geographical areas and of the existing/potentiallarge available bandwidth in the Ku/Ka band. Particularly inEurope, due to the successful introduction of digital videobroadcasting via satellite (DVB-S) [1], a promising techni-cal fundament has been laid for the development of satel-lite communications into these new market opportunitiesusing the second generation of DVB-S [2], commonly re-ferred to as DVB-S2, as well as return channel via satellite(DVB-RCS) [3] standards. Thus, for satellite systems cur-rently under development and being designed to supportmainly multimedia services, the application of the DVB-S2,for the high-capacity gateway-to-user (forward) links and ofDVB-RCS for the user-to-gateway (return) links, is widelyaccepted.

Complementing to satellite multimedia to fixed termi-nals, people are getting more and more used to broadbandcommunications on the move. Mobile telephones subscrip-tions have exceeded fixed line subscription in many coun-tries. Higher data rates for mobile devices are providedby new standards such as UMTS, high-speed packet access(HSPA), prestandardized version of mobile WiMAX, and, incase of broadcast applications, digital video broadcasting forhandhelds (DVB-H) [5].

At present, broadband access (e.g., to the Internet) anddedicated point-to-point links (for professional services) areprimarily supplied by terrestrial networks. Broadband sat-coms services are still a niche market, especially for mobileusers. In this context, many transport operators announcethe provision of TV services in ships, trains, buses, and air-crafts. Furthermore, Internet access is offered to passengers.With IP connectivity, also radio interfaces for GSM can beimplemented for such mobile platforms by using satelliteconnectivity for backhauling.

Thus, DVB-S2/RCS appears an ideal candidate to be in-vestigated for mobile usage, as it can ideally combine digitalTV broadcast reception in mobile environments (airTV, lux-ury yachts, trains, etc.) and IP multimedia services.


However, the aforementioned standards have not beendesigned for mobile use. Collective terminals installed in amobile platform, such as train, ship, or aircraft, are exposedto a challenging environment that will impact the system per-formance considering the current standard in absence of anyspecific provision.

Mobile terminals will have to cope in general with strin-gent frequency regulations (especially in Ku band), Dopplereffects, frequent handovers, and impairments in the synchro-nization acquisition and maintenance. Furthermore, the rail-way scenario is affected by shadowing and fast fading dueto mobility, such as, for example, the deep and frequentfades due to the presence of metallic obstacles along electri-fied lines providing power to the locomotive1 [6] and longblockages due to the presence of tunnels and large train sta-tions. This suggests that hybrid networks, that is, interwork-ing satellite and terrestrial components, are essential in orderto keep service availability.

In this context, this paper is focused on proposing andevaluating fade countermeasures to compensate the impactof fade sources in the railway scenario, that is, shadowing,fast fading, and power arches, excluding tunnels which willbe address at a later stage. In particular, antenna diversity andpacket level forward error correction (FEC) are investigated.

The rest of the paper is organized as follows: Section 2discusses the potential of opening the current DVB-S2/RCSstandards to provide mobile services efficiently. Section 3presents the peculiarities of the trains’ scenario and discussesthe different aspects that can impact the system performance.Section 4 describes the fade countermeasures proposed inthis paper. Section 5 introduces the simulation platforms inwhich the proposed fade countermeasures are evaluated andSection 6 presents and discusses the obtained results. Finally,Section 7 draws the conclusions of this work.

2. THE VISION: A NEW DVB-S2/RCS STANDARD FORMOBILE COLLECTIVE TERMINALS

The large capacity of DVB-S2/RCS systems can efficiently ac-commodate broadcast services (e.g., digital TV) and unicastIP multimedia interactive services to fixed terminals. How-ever, the increasing interest on broadband mobile servicessuggests that the natural evolution of DVB-S2/RCS standardto cover new market needs goes towards the support of mo-bile terminals.

In particular, the required antenna performance in Ku(10–12 GHz) and Ka (20–30 GHz) bands focuses the mar-ket opportunities of DVB-S2/RCS onto mobile terminals incollective transportation means. Actually, transport opera-tors are starting to announce the provision of TV services inships, trains, buses, and aircrafts, and broadband IP connec-tivity, for passengers. For the specific case of trains, broad-band services can provided using satellite systems, cellularconnectivity or dedicated trackside installations.

1 Hereafter referred to as “power arches,” for the sake of brevity.

As summarized in Table 1, none of these alternativesalone represents a satisfactory solution. As a matter of fact,deployed or upcoming commercial services are based oncombinations of different access technologies. In this light,a satellite access based on an open standard can have verysignificant benefits in terms of interoperability (achieved forDVB-S2/RCS through SatLabs Qualification Program) andcompetition, thus benefiting from availability of fully com-patible terminals from multiple vendors and reducing thecost of terminals.

However, the aforementioned DVB standards have beendesigned for fixed terminals. To cope with these new marketopportunities, DVB TM-RCS has investigated how the cur-rent DVB-RCS standard could be applied to mobile applica-tions. A white paper on the applicability of DVB-RCS to mo-bile services was prepared and a technical annex was addedto the implementation guidelines document [4]. This annexstates the boundary conditions and limitations under whichthe existing standard could be used in mobile environment,considering the impact of mobility in terminal synchroniza-tion and demodulator performance in forward and returnlinks. Furthermore, a survey on applicable regulations and abrief analysis on DVB-RCS features that can be used for mo-bility management are provided, the latter referring to inter-beam handover only.

Thus, the DVB-RCS guideline cannot support the fulladaptability to mobile environments and hence the applica-ble services and scenarios happen to be very limited. Fur-thermore, additional issues related to mobility are not fullysolved, such as handling of nonline-of-sight (nLOS) channelconditions, which will require the interworking with terres-trial gap fillers in the railway scenario due to the presence oftunnels. In addition, even if DVB-RCS features to be appliedfor mobility management are analyzed, a determined mech-anism or protocol should be specified in order to ensure in-teroperability. Finally, the impact of control signals loss (dueto deep fades or handover) is not negligible. For instance, theloss of terminal burst time plan (TBTP) tables damages theoperation of the resource management, essential in the re-turn link for a coordinated access to the radio resources.

As a matter of fact, mobile services could be more effi-ciently supported if the present standards could be improvedfor mobile scenarios. The reopening of the standard2 wouldallow for the specification of methods for improving the linkreliability in mobile environments (e.g., packet level FEC),handover protocols, interfaces to terrestrial gap fillers (evenusing terrestrial mobile technologies), improved mobility-aware signalling and resource management, and so forth.

In this context, a number of R and D initiatives are on-going with the aim at investigating enhancements of theDVB-S2/RCS standards for the efficient support of mobil-ity. Among those, the SatNEx network of excellence has setup a dedicated working group investigating different aspectsrelated to mobility in DVB-S2/RCS. The first results of thisactivity in the field of forward link reliability for the rail-way scenario are presented in this paper. For the return link,

2 Envisaged at the time of writing.

Stefano Cioni et al. 3

Table 1: Pros and cons of different solutions for providing broadband services on trains.

Type oftechnology

Examples Pros Cons

SatelliteDVB-S2/RCSProprietary systems,for example, ViaSat

(i) No new tracksideinfrastructure—quick todeploy, project costs may belower on long distance routes

(i) Available tracking antennas andefficient satcom modems expensive

(ii) Dedicated bandwidth available (ii) High variable cost per MB

(iii) Performance easy to predictdepending on satellite visibility

(iii) Return bandwidth constrainedby antenna size

(iv) Not affected by borders—goodfor international trains

(iv) Satellite visibility seriouslyrestricted on some rail routes

Cellular

GPRSEDGEUMTSHSUPA/HSDPA(EV-DO)

(i) Equipment is small and cheap (i) Geographic coverage of UMTSlimited for years to come

(ii) Usage is cheap (50–75 C per monthflat rate)

(ii) Coverage of railway lines oftenworse than roads

(iii) Data rates improving year on year (iii) GPRS/EDGE not really fast enough

(iv) Competitive supply—3 or 4 networkoperators in most countries

(iv) Inverse relationship betweenthroughput and train speed

(v) No QoS guarantees—affected bynetwork congestion at peak times

(vi) Organized country by country—dataroaming charges are punitive

TracksideFlash OFDMIEEE 802.11IEEE 802.16 (WiMAX)

(i) High data rates possible (i) Existing standards not designed tosupport fast-moving terminals

(ii) Can control bandwidth and QoS (ii) Proprietary equipment is moreexpensive

(iii) On-train equipment relativelyinexpensive

(iii) No suitable public services yet inlicensed bands—will licence-holders beallowed to provide mobile services?

(iv) No volume-related usage costs (iv) Licence-exempt bands are low power,thus limited range

(v) Infrastructure deployment (especiallytrackside) is expensive and time consuming

analogue solutions have to be devised, which are however notin the scope of the present work.

3. THE RAILWAY SCENARIO, A CHALLENGINGENVIRONMENT

3.1. Overview

The land mobile satellite channel (LMSC) has been widelystudied in the literature [7]. Several measurement campaignshave been carried out and several narrow and widebandmodels have been proposed for a wide range of frequencies,including Ku [8] and Ka [9] bands. Nevertheless, for the spe-cific case of the railway environment, only few results arepresented in [10] as a consequence of a limited trial cam-paign using a narrowband test signal at 1.5 GHz, performed

more than 10 years ago in the north of Spain. These resultsrepresent a very interesting reference, although no specificchannel model has been extracted from the collected data.After an initial qualitative analysis, the railway environmentappears to differ substantially with respect to the scenariosnormally considered when modelling the LMSC. Excludingrailway tunnels and areas in the proximity of large railwaystations, one has to consider the presence of several metallicobstacles like power arches (Figure 1, left uppermost), postswith horizontal brackets (Figure 1, left lowermost), whichmay be often grouped together (Figure 1, rightmost), andcatenaries, that is, electrical cables, visible in all the afore-mentioned figures.

The results of direct measurements performed along theItalian railway and aiming to characterize these peculiar ob-stacles are reported in [6] and references herein. In summary,


Figure 1: Nomenclature of railway specific obstacles.

the attenuation introduced by the catenaries (less than 2 dB)and by posts with brackets (2-3 dB) is relatively low and canbe easily compensated by an adequate link margin. On theother hand, the attenuation introduced by the power archesgoes, depending on the geometry, the radiation pattern of theRX antenna, and the carrier frequency, down to values muchgreater than 10 dB.

3.2. Modelling

Even if the layout and exact geometry of such obstacles cansignificantly change depending on the considered railwaypath, it turned out from previous works that the attenuationintroduced by these kind of obstacles can be accurately mod-elled using knife-edge diffraction theory [11]: in presence ofan obstacle having one infinite dimension (e.g., mountainsor high buildings), the knife-edge attenuation can be com-puted as the ratio between the received field in presence ofthe obstacle and the received field in free space conditions. Inthe case addressed here, as shown in Figure 2 (left), the obsta-cle has two finite dimensions, and the received field is hencethe sum of the contributions coming from both sides of theobstacle. Therefore, the resulting attenuation can be writtenas follows:

As(h)

= 1√2Gmax

(G(α1(h)

)∣∣∣∣∫∞Kh

e− j(π/2)v2dv∣∣∣∣

+ G(α2(h)

)∣∣∣∣∫ K(h−d)

−∞e− j(π/2)v2

dv∣∣∣∣)

,

K =√

2λ

a + b

a · b ,

(1)

where λ is the wavelength, a is the distance between the re-ceiving antenna and the obstacle, b is the distance betweenthe obstacle and the satellite, h is the height of the obstacleabove the line-of-sight (LOS), and d is the width of the ob-stacle. Finally, the usage of a directive antenna with radiationpattern G(α) has to be considered. This implies an additionalattenuation due to the fact that whenever the two diffractedrays reach the receiving antenna with angles α1 and α2 as

shown in Figure 2(left), the antenna shows a gain less thanthe maximum achievable (Gmax) and depending on the vari-able h, which is directly related to the space covered by thetrain.

In absence of a channel model directly extracted frommeasurements in the railway environment, it is a commonpractice to model the so-called “railroad satellite channel”by superimposing (i.e., multiplying) the statistical fades re-produced by a Markov model (see [8, 9]) with the space-periodic fades introduced by the electrical trellises obtainableby means of the above equation. Values of the parametersin Figure 2, as well as the space separation between subse-quent electrical trellises, depend on the considered railway.Finally, the considered receiving antennas are modelled withhigh directivity in order to achieve large gain and at the sametime to reduce the received multipath components with largeangular spread. Hence, as reported in [12], the key parame-ter becomes the antenna beamwidth which describes in thefrequency domain the Doppler power spectrum density ofthe satellite fading channel. In this paper, the highly direc-tive antennas are modelled with the reasonable value of thebeamwidth in the order of 5 degrees.

3.3. Need for fade countermeasures and gap fillers

The periodical fading events induced by power arches (PA)result in a physical error floor that limits the performance ofthe DVB-S2 system to unacceptable quality of service (QoS)levels. In Figure 3, the baseband frame (BBFRAME) errorrate is reported in LOS conditions, for train speed equal to300 km/h, and in the presence of power arches, when the re-ceiver has only one receiving antenna and does not adoptany packet level FEC technique. The error floor value isabout 0.0117, corresponding to the ratio between the du-ration of PA induced fading events, that is, 6 msillisecondsat 300 km/h, and the time between two fading events, thatis, 600 msilliseconds at 300 km/h. Considering the case of27.5 Mbaud, the DVB-S2 BBFRAME duration is less than1 msillisecond, therefore when the receiving antenna is ob-scured by a power arch, transmitted packets are completelylost unless fade countermeasures are adopted.

4. ADVANCED FADE COUNTERMEASURES

System designers can resort to different approaches to coun-teract deep fading conditions and to guarantee an acceptableQoS level. A possible classification of fade countermeasure isbetween those techniques that need a return channel (fromthe user to the network) to require a change in the transmis-sion mode or a retransmission of the lost information, andthose that do not rely on a return channel and are thereforemore suitable for unidirectional delivery, such as multicastor broadcast applications. The latter class of techniques is ofgreat interest for the collective railway application consideredin this work, for which return channel-based approaches,such as automatic repeat request (ARQ) or adaptive codingand modulation (ACM) techniques, are not doable. In par-ticular, antenna diversity and packet level FEC techniques areconsidered in the following.


b

hh-d

E2/E0 a E1/E0 v

α1α2

(a)

−45

−40

−35

−30

−25

−20

−15

−10

−5

0

5

Att

enu

atio

n(d

B)

−2.5 −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 2.5

h (m)

0.6 m0.4 m0.2 m

d = 0.4 m, a = 2.5 m

(b)

Figure 2: Knife-edge diffraction model applied to the railway sce-nario and possible attenuation caused by power arches at Ku bandfor different antenna diameters.

4.1. Antenna diversity

The adoption of multiple receiving antennas to counteractpower arch obstructions in railway environment has been re-cently proposed and investigated in [13, 14]. Antenna diver-sity is used to provide different replica of the received signalto the detector for combination or selection. If the receivingantennas are sufficiently spaced, the received signals fade in-dependently on each antenna thus providing multiple diver-sity branches that can be linearly or nonlinearly combined toimprove detection reliability. There are mainly three types oflinear diversity combining approaches: selection, maximal-ratio, and equal-gain combining. Considering two receiving

1E − 04

1E − 03

1E − 02

1E − 01

1E + 0

BB

FRA

ME

erro

rra

te

1 3 5 7 9 11 13 15 17 19 21

Eb/N0 (dB)

1/2 - QPSK (LOS, FAST, noPA)2/3 - 8PSK (LOS, FAST, noPA)3/4 - 16APSK (LOS, FAST, noPA)5/6 - 16APSK (LOS, FAST, noPA)1/2 - QPSK (LOS, FAST, PA)2/3 - 8PSK (LOS, FAST, PA)3/4 - 16APSK (LOS, FAST, PA)5/6 - 16APSK (LOS, FAST, PA)

Power arches floor

Figure 3: BBFRAME error rate for DVB-S2 in the presence ofpower arch blockage events. LOS propagation conditions and trainspeed set to 300 km/h.

antennas, and assuming perfect compensation of time delaysof the two replicas, the combined signal can be written as

rc(t) = w1r1(t) + w2r2(t), (2)

where wi and ri(t), i = 1, 2, are the combing weights andthe received signals, respectively. The received signals at eachantenna is

ri(t) = αis0(t) + ni(t), (3)

where s0(t) is the transmitted signal, αi is the time variantfading envelope over the ith antenna, and ni(t) is the thermalnoise.

The simplest combining scheme is the signal selectionCombining (SC), in which the branch-signal with the largestamplitude or signal-to-noise ratio (SNR) is the one selectedfor demodulation. In this case, wi will be 1 or 0 if theith power branch is the largest or the smallest, respectively.Clearly, SC is bounded by the performance of the single re-ceiving antenna in absence of fading, that is, there is no di-versity gain when the two antennas experience good chan-nel conditions at the same time. Maximum-ratio combin-ing (MRC), although requiring a larger complexity at thereceiver, allows for the exploitation of the diversity gain. Infact, MRC scheme provides for the maximum output SNR.According to the optimum combination criterion, the signalweights are directly proportional to the fading amplitude andinversely proportional to the noise power, Ni, as follows:

wi = αiNi

. (4)

Another technique, often used because it does not requirechannel fading strength estimation, is equal gain combining


(EGC) in which the combination weights are all set to one,thus leading to a simpler but suboptimal approach. Clearly,SC and MRC (or EGC) represent the two extremes in diver-sity combining strategy with respect to the complexity pointof view and the number of signals used for demodulationprocess. Furthermore, the classical combining formula canbe generalized for nonconstant envelope modulations suchas 16-APSK or 32-APSK (amplitude and phase shift keying)and integrated with the soft demodulator that computes thechannel a posteriori information to feed the low density par-ity check (LDPC) FEC decoder. The maximum likelihood apriori information for a single receiver antenna given by

log

(Pr{bi = 0 | rk

}Pr{bi = 1 | rk

})

= log

(∑si∈S0

exp(−∣∣rk − αksi

∣∣2/N0

)∑

si∈S1exp

(−∣∣rk − αksi∣∣2/N0

)) (5)

can be extended for L receiving antennas, according to theMRC principle, as follows:

log

(Pr{bi = 0 | rk

}Pr{bi = 1 | rk

})

= log

(∑si∈S0

exp(−∑L

p=0

(∣∣r pk − αpk si∣∣2/N

p0

))∑

si∈S1exp

(−∑Lp=0

(∣∣r pk − αpk si∣∣2/N

p0

)))

,

(6)

where rk is the received sample at time k, αk is the true orthe estimated channel coefficient, and S0 and S1 are the setsof symbols which have “0” or “1” in the ith position, respec-tively.

In the configuration proposed in this work, we adoptMRC combining with two antennas. The antennas are placedon the same coach so as to reduce the costs of installa-tion and the connection length. The antenna spacing is cho-sen as a function of the distance between two consecutivepower arches so as to guarantee that only one antenna ata time can be obscured. Accordingly, the distance betweenthe two antennas is about 15 m. Considering the maximumtrain speed (about 300 km/h), this translates into the factthat power-arch blockage on a single antenna lasts for about7 msilliseconds, and it hits the second antenna after about180 msilliseconds. Therefore, it is reasonable to assume thatthere is enough time for the combining circuit to react andmaintain constant signal connection. A drawback of this ap-proach is that the receiving chain will be duplicated in or-der to maintain connection and avoid frequent reacquisitionsprocess with the consequent loss of packet. As proposed in[14], the solution which considers the presence of a secondreceiving antenna is depicted in Figure 4. The gray blocksrepresent the subsystems that need to be duplicated in thetwo antenna case. Further details on the digital receiver aredescribed in Section 5.1.

4.2. Packet level FEC

4.2.1. The concept of packet level FEC

Reliable transmission occurs when all recipients correctly re-ceive the transmitted data. This target can be achieved by op-erating at different layers of the protocol stack and in dif-ferent ways. Retransmission techniques allow that lost pack-ets are retransmitted to the receivers, while packet level FECschemes create redundant packets that permit to reconstructthe lost ones at the receiver side, with a very beneficial in-put on the final end-to-end delay. In fact, as detailed in [15],the additional delay introduced by packet level encoding anddecoding is always lower than the delay deriving from anyretransmission scheme.

Regarding the retransmission schemes, efficient proto-cols should limit the use of acknowledgement- (ACK-) basedmechanisms because they introduce heavy feedback traffictowards the sender, thus increasing the congestion of reverselink that, typically, has a reduced capacity with respect toforward link. Negative acknowledgement- (NACK-) basedapproaches are hence particularly interesting. In combina-tion with (or in alternative to) the traditional retransmissionschemes, packet level FEC can be added on top of physicallayer FEC, in order to achieve the same level of reliability witha reduced number of retransmissions. This might be partic-ularly useful if resources on the return link need to be saved(smaller number of NACKs or no NACKs are needed at all),or when multiple lost packets are recovered with the retrans-mission of a lower number of redundant packets. Basically,h redundancy packets are added to each group of k informa-tion packets, thus resulting in the transmission of n = k + hpackets. These packets are finally transferred to the physi-cal layer, which adds independent channel coding to each ofthem. This principle is described in Figure 5.

At the physical layer, the bits affected by low noise lev-els can be corrected by the physical layer FEC, so that therelated packets are passed to the higher layer as “correct.” Ifthe noise level exceeds the correcting capability of the phys-ical layer, the received bit cannot be properly decoded, butthe failure to decode can be usually detected with a very highreliability. Since erroneous packets are not propagated to thehigher layers, we have an erasure channel. The system can usethe redundancy packets to recover these erasures. By usingmaximum distance separable (MDS) codes, like the Reed-Solomon, it is possible to reconstruct the original informa-tion if at least k out of n packets are correctly received. There-fore, the receiver can cope with erasures, as long as they resultin a total loss not exceeding h packets, independently fromwhere the erasures occurred. LDPC codes and their deriva-tions might be also used because of their low complexity andgreater flexibility, thus permitting to encode larger files, al-though a small inefficiency, depending on the code designand typically around 5%–10%, will be taken into account.

If packet level FEC is implemented at IP or data link layer,very near to the physical channel, no change in the trans-port and network layers protocols and in the physical layerare necessary. This solution presents the additional advantagethat it can be adapted to the propagation channel conditions


Framesynch

Receivedsignalfrom

antenna no. 1

Matchedfilter

Symbolsampling DeMUX

DataBuffer

Frequencyacquisition

Timingrecovery

Preamble /pilots

Noise levelestimation

N10

θ10

α1k

θ10

θ1k

DigitalAGAC

BufferLock

detector

Freq./phasetracking

Signalcombiner

Hard/softdemodulator

De-interleaver

LDPC/BCHdecoder

From secondantenna

Figure 4: Receiver block diagram with antenna diversity.

n packets

k data packets (group) h redundancy packets

1 2 · · · k k + 1 · · · k + h Data link/IP layer

Channel coding

1 2 · · · k k + 1 · · · k + h Physical layer

Transmission

Figure 5: Packet level FEC principle.

by choosing n, so that the interleaver size is long enough tocompensate the channel outages. However, different protec-tion for individual transfers (e.g., specific files) is not possi-ble (although different QoS classes may be supported), extramemory is required, and additional delays must be properlyhandled.

For the forward link, the usage of packet level FEC isespecially powerful in allowing online variable coding ap-proaches, which can be fine tuned in a closed-loop approach.Based upon the “history” of the link, appropriate redun-dancy can be easily added. Packet level FEC has then impacton different layers.

(i) The requirements on control loops can be lessened, forexample, power control and or adaptive coding andmodulation control, if a loss of up to h packets can tol-erated.

(ii) The typical fade structure of a link can be measuredand accordingly coding with the correct profile added.

(iii) Different QoS classes with different redundancy pro-files can be supported. Furthermore, redundancypackets for low-priority traffic can be put in a specialqueue, which is served only if free capacity is availableand, in turn, increased redundancy can be sent duringhandovers, minimizing the overall probability of lostpackets.

(iv) Different IP-based access methods can be used in par-allel, improving the link reliability if different redun-dancy is sent via different access methods.

4.2.2. The GSE-FEC method

When moving to the concrete applicability of this scheme tothe scenario under consideration, even though the fact thatIP packets have three sizes that are the most common ones,the fact that IP packet size can actually take any value upto a maximum value (typically 64 Kbytes) represents a clear


IP packetsFEC matrix GSE

encapsulation

BBFRAME assemblyusing one or several

GSE units

BBFRAMEpadding

BBFRAMEs

Figure 6: Steps involved in GSE-FEC.

difficulty in applying packet level FEC (PL-FEC). The funda-mental difficulty comes from the fact that most codes take asinput a fixed amount of data, from which they compute theredundancy bytes. As a given number of IP packets corre-spond to a variable amount of data depending of their sizes,codes needing a fixed amount of data cannot be directly ap-plied. One possible solution is to use codes that can be eas-ily adapted to different input sizes; however, this comes atthe price of a much more complex encoding and decodingprocess. Another solution has been proposed in the DVB-Hstandard [16]. In this case, units of constant length are builtby interleaving IP packets and, therefore, codes with fixed in-put size can be easily applied. It is worth noting that thoseunits are not built by concatenating IP packets but by inter-leaving them. However, interleaving is this case must not beunderstood as it is typical in physical layer coding, where itmeans that data is written in one direction in a matrix andit is read in the orthogonal direction for transmitting. In PL-FEC, we understand interleaving as computing the redun-dancy in an orthogonal direction to the writing direction ofthe data; however, in this case the writing and reading direc-tions coincide. This kind of interleaving is advantageous be-cause the redundancy is computed across a large number ofpackets. Thus, a fade event may destroy one or several pack-ets but not the majority of them, assuming that the systemis well dimensioned, so the added redundancy can effectivelyhelp in recovering the destroyed packets.

DVB-H also provides a solution for encapsulating thecoded IP packets for transmission over DVB-T. The solutionis based on the use of multiprotocol encapsulation (MPE)combined with MPEG. Although it would be possible toadapt the same approach for DVB-S2, it presents a numberof drawbacks, such as lack of flexibility, low encapsulationefficiency, delay constraints. A new encapsulation protocolcall generic stream encapsulation (GSE) has been recently de-fined [17]. It is a very flexible protocol applicable to severalphysical layer standards. It overcomes most of the limitationsof MPE-MPEG. GSE is especially suitable for transmitting IPpackets through the generic stream interface mode of DVB-S2, and it has been proposed for the second generation ofTerrestrial digital video broadcasting (DVB-T2) as well. GSEalso efficiently supports the ACM functionalities of DVB-S2and facilitates the provision of QoS guarantees because it re-duces the constraints on the scheduling operation.

It can be deducted from the previous discussion that theimplementation of PL-FEC consists of two main processes:the encoding the IP packets and, second, the encapsulationof the result of the encoding process in order to adapt it tothe underlying transmission system. In DVB-H, the first pro-cess consists in arranging the IP packets in a matrix (here-after called FEC matrix) and applying a Reed-Solomon code,

while the second process employs MPE-MPEG. The wholeimplementation is called MPE-FEC in DVB-H. Our proposalfor DVB-S2 is based on keeping the same first process as inDVB-H, whereas it employs GSE in the second process. Thisproposal for applying PL-FEC in DVB-S2 is named GSE-FEC.

A block diagram of GSE-FEC is depicted in Figure 6. Theincoming IP packets are arranged in the so-called FEC ma-trix, where also the packet-level redundancy is added. Thefilling of the FEC matrix and the encoding are done in thesame way as in DVB-H. For the sake of completeness, thiswill be briefly described below. Next, each IP packet is en-capsulated using GSE, and this represents one of the novelaspects of our proposal. Each IP packet may be fragmentedinto several GSE units or it may also be sent unfragmented.Subsequently, the maximum number of GSE units that canbe fitted inside a BBFRAME is concatenated and introducedin the BBFRAME. The size of the BBFRAME depends on thecombination of coding rate and modulation scheme (MOD-COD) adopted by the DVB-S2 modem, so the number ofGSE units that can be concatenated also depends on theMODCOD. By making the GSE units small enough to havethe required flexibility, but large enough in order not to pe-nalize encapsulation efficiency, this method provides an easymechanism to adapt the output of the packet-level FEC to thevariations of the physical layer. Moreover, note that paddingis not applied inside the GSE unit but only at BBFRAME levelif the size of the BBFRAME does not coincide with that of theconcatenation of the GSE units.

The IP packets are placed one after another along thecolumns of the FEC matrix, see Figure 7. Each IP packet maybe split among two or more columns. Only the first block ofthe matrix, from column 1 to 191, can be filled in with IPpackets. The second block of the matrix, from column 192 to255, carries the redundancy information, which is computedby a Reed-Solomon (255,191) code applied to the first blockon a row basis. Each column in the second block is encap-sulated individually using GSE, whereas in the first block theGSE encapsulation is performed on an IP packet basis. In thebaseline operation, padding is only applied in the first blockto account for the fact that an additional IP packet may notbe fitted without overrunning the 191 columns and all 64 re-dundancy columns are transmitted. The code can be madeweaker (i.e., with higher rate) by puncturing some of the re-dundancy columns, which are then not transmitted and areconsidered as unreliable bytes in the decoding process. Thecode can also be made more robust (i.e., with lower rate)by padding with zeros columns in the first block and, hence,leaving less space for IP packets. The padded columns are nottransmitted but they are used in the encoding process. In thedecoding process, they are considered as reliable.


Coding direction

Wri

tin

gdi

rect

ion

FEC matrix

1 2 3 188 189 190 191 192 193 254 255

· · · · · ·

Data submatrix Redundancy submatrix

IP packet encapsulation with GSE Percolumn GSE encapsulation

Col

um

nsi

ze

IPpa

cket

1

IPpa

cket

2IP

pack

et1

(con

t.)

IPpa

cket

3IP

pack

et2

(con

t.)

Padd

ing

Las

tIP

pack

et(c

ont.

)

Padd

ing

Padd

ing

Padd

ing

1st

redu

nda

ncy

colu

mn

2nd

redu

nda

ncy

colu

mn

Pu

nct

ure

dco

lum

n

Pu

nct

ure

dco

lum

n

Figure 7: Arrangement of IP packets for FEC encoding.

After GSE encapsulation, the GSE packets are introducedin BBFRAMEs and transmitted. On the receive side, erro-neous BBFRAMEs are detected by checking the CRC. Thereceiver reconstructs the FEC matrix and marks any columnthat is totally or partially received by means on an erroneousBBFRAME as unreliable. Finally, if the reconstructed FECmatrix has no more than 64 unreliable columns, the codecan correctly compute all bytes in the matrix. If there aremore than 64 unreliable columns, the code cannot correctanything, and only those columns received by means of cor-rect BBFRAMEs will be correct.

5. SIMULATION SCENARIOS

In the following, the simulation platforms used to evaluatethe performance of DVB-S2 with advanced fade countermea-sures in the railway environment as described in Section 3 areduly detailed.

5.1. Advanced physical layer simulation platform

To cover a rather large set of spectral efficiency, four MOD-CODs have been considered: 1/2-QPSK, 2/3-8PSK, 3/4-16APSK, and 5/6-16APSK. The LOS channel condition(Rice factor equal to 17.4 dB) and the train speed equal to300 km/h have been simulated. Equally spaced power archeswith a separation of 50 m have been included in some sce-narios, with a duty cycle of 1%, corresponding to a width of0.5 m in accordance with Figure 2. The symbol rate was fixedto 27.5 Mbaud.

The considered DVB-S2 physical layer transmitter [2] isdepicted in Figure 8. A continuous stream of MPEG pack-ets passes through the mode adaptation which providesinput stream interfacing. This data flow is passed to the

merger/slicer that, depending on the applications, allocatesa number of input bits equal to the maximum data field ca-pacity. In this way, user packets are broken in subsequentdata fields, or an integer number of packets are allocated init. Then, a fixed length base-band header (BBHEADER) of80 bits is inserted in front of the data field, describing its for-mat. For example, it reports to the decoder the input streamsformat, the mode adaptation type and the roll-off factor.The efficiency loss introduced by this header varies from0.25% to 1% for long and short codeword lengths, respec-tively. The role of stream adaptation is to provide paddingwhen needed, in order to complete a constant length frame,and scrambling. Padding is applied when the user data avail-able for transmission are not sufficient to completely fill aBBFRAME, or when more than one packet have to be allo-cated in a BBFRAME. The built frame is randomized using ascrambling sequence generated by the pseudorandom binarysequence described by the polynomial (1 + X14 + X15). Afterthis scrambling, each BBFRAME is processed by the forwarderror correction (FEC) encoder which is carried out by theconcatenation of a Bose-Chaudhuri-Hocquenghem (BCH)outer code and an LDPC inner code. Available code-ratesfor the inner code are 1/4, 1/3, 2/5, 1/2, 3/5, 2/3, 3/4, 4/5,5/6, 8/9, and 9/10. Depending on the application area, code-words can have length NLDPC = 64800 bits or 16200 bits. Inthe following, the case of 64800 bits is considered. Regard-ing the modulation format, each coded BBFRAME can bemapped onto QPSK, 8PSK, 16APSK, or 32APSK constella-tions. Modulated streams enter in the physical layer framingwhere physical layer signalling and pilot symbols are inserted.For energy dispersal, another scrambling sequence is appliedto the entire physical layer frame (PLFRAME). The systemhas been designed to provide a regular PLFRAME structure,based on slots of M = 90 modulated symbols, which allow


Single/multipleinput data streams

Inputinterface no. 1

BBsignaling

Mergeslicer

Streamadapter

Inputinterface no. n

...

Mode & streamadaptation

1/4, 1/3, 2/5,1/2, 3/5, 2/3,3/4, 4/5, 5/6,

8/9, 9/10

BCHLDPC

bit interleaver

FEC coding

QPSK8PSK

16APSK32APSK

Mapping

PL signalingpilot symbols

Scrambler

Dummyframe

PL framing

Roll-off factors:α = 0.2,α = 0.25,α = 0.35

BBfilter

Modulation

BBFRAME FECFRAME PLFRAME To the RFsatellitechannel

Figure 8: DVB-S2 physical layer transmitter block diagram (taken from [2]).

reliable receiver synchronization on the FEC block struc-ture. The first slot, PLHEADER, is devoted to physical layersignalling, including start-of-frame (SOF) delimitation andMODCOD definition. Receiver channel estimation is facil-itated by the introduction of a set of P = 36 pilot sym-bols, that are inserted every 16 slots. In addition, a pilot-less transmission mode is also available, ensuring greater sys-tem capacity. Finally, for shaping purposes, a squared-rootraised cosine (SRRC) filter with variable roll-off factors (0.2,or 0.25, or 0.35) is considered. To cope with the intrinsicnonlinearity of the on-board high power amplifier (HPA),a purposely designed predistortion technique is considered.In particular, a fractional predistortion technique based ona lookup table (LUT) approach is considered which operatesright after the shaping filter [18]. The fractional predistorter,which is a digital waveform predistorter, acts on the signalsamples for precompensating the HPA AM/AM and AM/PMcharacteristics and mitigating the impact of non linear dis-tortion. In particular, the signal is processed by means ofthe LUT, which stores the inverted HPA coefficients com-puted offline through analytic inversion of a proper HPAmodel. The steps needed to obtain LUT coefficients are thefollowing: HPA model selection, parameter extrapolation, an-alytical model inversion, and LUT construction. Regarding thefirst step, a simple yet robust empirical model is the clas-sic Saleh model [18]. Given the measured HPA character-istics, the second step can be performed by minimizing theenergy of the difference between the modelled and the ex-perimental HPA curves (MMSE criterion). These parametersare then applied to the analytically inverted characteristics,so as to obtain the analytical predistortion transfer function.The last step is the quantization of the analytical curve inorder to store it into the LUT. The adopted strategy is lin-ear in power indexing, that is, table entries are uniformlyspaced along the input signal power range, yielding densertable entries for larger amplitudes, where nonlinear effectsreside.

The proposed digital receiver architecture is depicted inFigure 4. In particular, several subsystems are present in or-der to coherently demodulate and combine the received sig-nals. The first coarse correction regards the carrier frequency,

which allows match filtering with minimal intersymbol in-terference regrowth; then the subsequent block deals withclock recovery for timing adjustment, performed by a digi-tal interpolator. The demultiplexer is used to separate pilotsfrom data symbols in a PLFRAME. The pilot symbol streamis used by the following four subsystems: the noise level esti-mator, the digital automatic gain and angle control (AGAC),the block in charge of tracking the residual frequency offsetand carrier phase, and finally the coarse frequency acquisi-tion loop (not performed). On the other path, the data sym-bols, softly combined with the last equation of Section 4.1,feed the hard/soft demodulator. The demodulator providesthe hard decisions on data symbols as a feed-back for car-rier frequency and phase tracking, and computes the soft ini-tial a posteriori probability (APP) on the received informa-tion bits. Finally, the APPs are deinterleaved and given to theLDPC-BCH decoder. As far as frame synchronization andfrequency acquisition are considered, that is, dashed whiteblocks in Figure 4, they are not considered in the simula-tion chain because the receiver behaviour is assessed duringsteady state.

5.2. Packet level coding simulation platform

A simulation platform to analyze the performance of GSE-FEC has been developed. Given that this performance as-sessment entails many layers, in particular, from the physicalto the network layers, of the protocol stack, a modular ap-proach has been considered as the only feasible way to de-velop the platform. The physical-layer simulator describedin the previous section interfaces with the packet-level sim-ulator shown in Figure 9. This takes as input a stream ofIP packets and applies the GSE-FEC encoding technique asdescribed above, generating a sequence of BBFRAMEs. Atthis point, the output of the physical-layer simulator is usedto mark the BBFRAMEs as correctly or wrongly received.Next, the GSE-FEC decoding process is applied. The effectof the BBFRAMEs on the GSE units and subsequently on thecolumns of the reconstructed FEC matrix is calculated. Then,the correction capability of the Reed-Solomon code is takeninto account to eliminate, if possible, the unreliable columns


Traffic generation

IP packets

GSE-FEC

BBFRAMEs

Selective BBFRAMEcorruption

Physical-layersimulation

Time series ofcorrect/wrong BBFRAMEs

IP PERcalculation

Mapping tocorrect/wrong

IP packets

Corrected FECmatrix

FEC decoding


FEC matrixcolumns


GSE units

Figure 9: Simulation platform at IP-BBFRAME level.

of the FEC matrix. Finally, the list of IP packets affected bythe unreliable columns (an IP packet is considered wrong ifany part of it falls inside an unreliable column which cannotbe corrected) is obtained and the packet error rate (PER) atIP level is computed.

The packet-level simulator is useful to assess very quicklythe performance of different parameter configurations ofthe GSE-FEC since different combinations can be simulatedwithout the need of repeating the time-consuming physicallayer simulations. The main parameters of GSE-FEC to bedesigned are the following:

(i) size of the columns of the FEC matrix,(ii) size of GSE units,

(iii) number of padding columns in the first part of the FECmatrix,

(iv) number of punctured redundancy columns.

The effect of varying some of these parameters will be shownin the numerical results section.

6. RESULTS

6.1. Antenna diversity

Numerical results have been obtained by considering theentire transmit-receive chain described in Section 5.1. Theintroduction of the second receiving antenna adopting the

1E − 04

1E − 03

1E − 02

1E − 01

1E + 0

PE

R

−2 −1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Eb/N0 (dB)

1/2 - QPSK (LOS, FAST, noPA)2/3 - 8PSK (LOS, FAST, noPA)3/4 - 16APSK (LOS, FAST, noPA)5/6 - 16APSK (LOS, FAST, noPA)1/2 - QPSK (LOS, FAST, MRC)2/3 - 8PSK (LOS, FAST, MRC)3/4 - 16APSK (LOS, FAST, MRC)5/6 - 16APSK (LOS, FAST, MRC)

Power arches floor

Figure 10: MRC performance in LOS channel condition and trainspeed equal to 300 km/h.

MRC technique is reported in Figure 10. The most impor-tant result is that the MRC solution completely eliminatesthe error floor with respect to the single antenna case (seefor comparison Figure 3). Secondly, it will be observed thatinstead of a constant 3- dB gain for all Eb/N0 values, threedifferent working regions can be distinguished. In particular,BBFRAME error rates curves are characterized by two water-fall regions separated by a short floor. This unexpected be-haviour has a theoretical explanation that has been treatedin details in [14]. Here, we limit the discussion to a numeri-cal example. Let us consider MODCOD = 1/2-QPSK and aworking Eb/N0 = 0 dB, when a PA blockage event occurs, the“nonobscured” antenna has not a sufficient SNR to reliablydecode the received MPEG packets, thus generating an errorfloor at that Eb/N0. The second waterfall region starts onlyfor Eb/N0 values larger than 1 dB, when, as a matter of fact,a single antenna receiver has sufficient margin to correctlydecode. This consideration can also be extended to all otherMODCOD configurations. Notably, the short floor value istwice the floor value obtained with one receiving antenna;this is determined by the fact that there are two blockageevents between two consecutive PA, that is, one per receiv-ing antenna.

6.2. Packet level FEC

The objective of the following analysis is twofold: first, toprovide a guideline for an appropriate choice of the columnsize of the FEC matrix, which is the key parameter in theGSE-FEC method; second, to analyze the performance ofGSE-FEC under various configurations. In all cases, a sce-nario with line-of-sight propagation has been used.


0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Pro

babi

lity

0 2 4 6 8 10 12 14

Error burst length

1/2-QPSK

(a)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Pro

babi

lity

0 2 4 6 8 10 12 14

Error burst length

2/3-8PSK

(b)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Pro

babi

lity

0 2 4 6 8 10 12 14

Error burst length

5/6-16APSK

(c)

Figure 11: Histogram of the BBFRAME error burst length for two different MODCOD modes and target BBFRAME error rate equal to0.02.

6.2.1. Dimensioning the FEC matrix

First of all, it is worth remarking that the appropriate sizeof the FEC matrix depends on the length of the bursts oferroneous BBFRAMEs. It is clear that longer bursts will re-quire larger FEC matrices to avoid that the number of wrongcolumns exceeds the correction capability of the code. There-fore, the design of the height of the FEC matrix should bederived from an analysis of the length of the error bursts.Figure 11 shows the histogram of the length of the bursts forsome particular MODCOD modes for the scenario describedabove. In all modes besides the two shown in Figure 11,it is observed that the distribution is bimodal. The burstsof short length (typically between 1 and 4 BBFRAMEs) aredue to random errors caused by noise, whereas the rest ofbursts are caused by the power arches. Second, the higherthe modulation order, the longer the error bursts producedby power arches are. This is justified by the fact that ac-cording to the DVB-S2 standard, BBFRAMEs are coded andconverted into FECFRAMEs, which have constant lengthin bits regardless of the used modulation [2]. The bits inthe FECFRAME are transformed by the modulator intobytes in the PLFRAMEs. Higher modulations need fewersymbols and, hence, less time to transmit an FECFRAME.The duration of the fade event caused by a power archonly depends on the speed of the train, which we haveconsidered to be 300 km/h throughout the rest of the pa-per. Therefore, the shorter the PLFRAME, the more PL-

FRAMEs and hence BBFRAMEs are affected by each powerarch.

In order to present the procedure to compute the col-umn size of the FEC matrix, we consider a numerical exam-ple. We use for instance the least efficient MODCOD, thatis, 1/2-QPSK. It can be seen in Figure 11 that the maximumerror burst length due to power arches is 7 BBFRAMEs. Inthis MODCOD, each BBFRAME has a data field of length32128 bits [2], which is equal to 4016 bytes. Therefore, aburst of 7 BBFRAMES corresponds to 28112 bytes. We con-sider that this amount of bytes should correspond to lessthan 30 columns in the FEC matrix. The value of 30 hasbeen chosen arbitrarily. It is nevertheless a reasonable num-ber since the objective is to leave a margin with respect to the64 columns that the code can correct (assuming no punctur-ing) so as to be able to cope with errors caused by noise aswell. Therefore, the column size of the FEC matrix shouldfulfil

30Lc ≥ 28112 =⇒ Lc ≥ 938 bytes, (7)

where Lc is the number of rows (i.e., the length of each col-umn) of the FEC matrix in bytes. In the previous compu-tation, we have not taken into account the overhead intro-duced by GSE since it is small and we are only interestedin obtaining an approximate value for the column size. Ifthe same calculation is repeated for the most efficient MOD-COD, that is, 5/6-16APSK, the result is Lc ≥ 2912 bytes. The


0

0.02

0.04

0.06

0.08

0.1

0.12IP

pack

eter

ror

rate

0 1000 2000 3000 4000 5000 6000

Column size (bytes)

1/2-QPSK

(a)

0

0.02

0.04

0.06

0.08

0.1

0.12

IPpa

cket

erro

rra

te

0 1000 2000 3000 4000 5000 6000

Column size (bytes)

2/3-8PSK

(b)

0

0.02

0.04

0.06

0.08

0.1

0.12

IPpa

cket

erro

rra

te

0 1000 2000 3000 4000 5000 6000

Column size (bytes)

3/4-16APSK

(c)

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

IPpa

cket

erro

rra

te

0 1000 2000 3000 4000 5000 6000

Column size (bytes)

5/6-16APSK

(d)

Figure 12: Comparison of the IP packet error rate for different ACM modes in a channel with BBFRAME error rate equal to 12% (circles→results without any kind of PL-FEC, squares→ results with GSE-FEC).

results for the intermediate MODCODs, 2/3-8PSK and 3/4-16APSK, are 1790 and 2618 bytes, respectively.

We conclude from this discussion that the appropriatesize of the FEC matrix strongly depends on the error burstlength caused by the power arches, which in its turn dependson the train speed. The lower the train speed is, the longerthe bursts are and the taller the FEC matrix must be. How-ever, the size of the FEC matrix cannot be increased arbitrar-ily because it has an impact on the delay of GSE-FEC processand, on top of that, because more errors due to noise appearinside the FEC matrix. These errors may risk the correctioncapability of the code, as will be seen below. Therefore, theperformance of GSE-FEC may be limited for low train speedssince it is not possible to combat simultaneously very long er-ror bursts due to power arches and a large amount of randomerrors due to noise.

6.2.2. Performance analysis

Dependence on the size of the FEC matrix

The IP packet error rate as a function of the column size fordifferent MODCODs is shown in Figures 12 and 13. The con-sidered columns sizes and the corresponding number of GSEunits used to encapsulate each RS redundancy column arelisted in Table 2. The number of GSE units per column hasbeen selected in such a way that the size of the units is smallenough to limit the amount of padding in the BBFRAMEs,but large enough not to penalize encapsulation efficiency(encapsulation efficiency is out of the scope of this work andwill be analyzed in a follow-on paper). A fixed IP packetlength equal to 576 bytes has been considered.


0

0.005

0.01

0.015

0.02

0.025

IPpa

cket

erro

rra

te

0 1000 2000 3000 4000 5000 6000

Column size (bytes)

1/2-QPSK

(a)

0

0.005

0.01

0.015

0.02

0.025

IPpa

cket

erro

rra

te

0 1000 2000 3000 4000 5000 6000

Column size (bytes)

2/3-8PSK

(b)

0

0.005

0.01

0.015

0.02

IPpa

cket

erro

rra

te

0 1000 2000 3000 4000 5000 6000

Column size (bytes)

3/4-16APSK

(c)

0

0.005

0.01

0.015

0.02

0.025

0.03

IPpa

cket

erro

rra

te

0 1000 2000 3000 4000 5000 6000

Column size (bytes)

5/6-16APSK

(d)

Figure 13: Comparison of the IP packet error rate for different ACM modes in a channel with BBFRAME error rate equal to 2% (circles →results without any kind of PL-FEC, squares→ results with GSE-FEC).

Figures 12 and 13 also compare the results obtained whenGSE-FEC is used and when no packet-level FEC is applied.The baseline GSE-FEC is employed, that is to say, no ad-ditional padding has been used in the first 191 columnsand no puncturing of the last 64 columns has been per-formed. The case of no packet-level FEC follows the samearchitecture as for GSE-FEC, depicted in Figures 6 and 7.The difference is that the 255 columns of the FEC ma-trix are filled with IP packets and no redundancy is intro-duced into it. Figure 12 was obtained when the physical-layer simulator was tuned to provide a BBFRAME error ratearound 0.12, whereas Figure 13 was obtained for a valueof 0.02.

In the case of no packet-level FEC, the IP PER is almostinsensitive to changes in the column size and its value is veryclose to the BBFRAME error rate, as expected. It is very in-teresting to observe that the proposed scheme, GSE-FEC, ef-fectively reduces the IP PER and, in many configurations, theIP PER is exactly zero.3 This means that, in those cases, all

3 Note that the simulation duration was equal to 5000 BBFRAMEs, so wecan only say that the IP PER is not worse than 2× 10−5.

IP packets were correctly received in spite of the fact that theBBFRAME error rate is higher than 10%.

For small column sizes, the IP PER decreases as the col-umn size increases. This behaviour is in line with the discus-sion at the beginning of this section: when the FEC matrixis too small, a power arch causes errors in a portion of thematrix that is too large to be corrected by the code. The IPPER decreases until it reaches a minimum, which is attainedat a column length that is well approximated by the previ-ous back-of-the-envelope calculations. If the column lengthis increased further, the IP PER increases because the correc-tion capability of the code is fixed and equal to 64 columns,but the size of the FEC matrix becomes larger and, hence,the number of errors due to noise increases. This behaviouris visible in Figure 12, but not in Figure 13. The reason isthat the later figure corresponds to a scenario with very highsignal-to-noise ratio, and BBFRAME errors are almost onlycaused by power arches.

Dependence on the IP packet length

The effect of different IP packet lengths is shown in Figure 14.In this case, the column size of the FEC matrix is fixed


0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

IPpa

cket

erro

rra

te

0 500 1000 1500

IP packet length (bytes)

1/2-QPSK

No PL-FECColumn size: 1024 bytesColumn size: 4096 bytes

(a)

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

IPpa

cket

erro

rra

te

0 500 1000 1500

IP packet length (bytes)

5/6-16APSK

No PL-FECColumn size: 1024 bytesColumn size: 4096 bytes

(b)

Figure 14: Dependence of the IP packet error rate with the IP packet size for two column sizes (1024 and 4096 bytes) and two MODCODmodes (1/2-QPSK and 5/6-16APSK).

and equal to 1024 or 4096 bytes. The general trend is thatthe IP PER slightly increases as the IP size increases. Thereare however some lengths, such as 576 bytes, that are espe-cially favourable. This happens because for those lengths aninteger number of IP packets fit in an integer number ofcolumns of the FEC matrix. For instance, it is fulfilled that576 × 16 = 1024 × 9, which means that 16 IP packets oflength 576 bytes fit in 9 columns of length 1024 bytes. As thisperfect fitting reduces the ratio of IP packets that are splitacross two columns, the number of IP packets corrupted bya wrong column is also reduced on average. If the length ofIP packets follows a certain distribution, as it happens withreal traffic, the IP PER can be obtained by computing an av-erage of the values shown in Figure 14. This average wouldbe computed by weighting the IP PER for a given length bythe frequency of occurrence of that length.

Conclusions on GSE-FEC results

The analysis of the GSE-FEC and the corresponding numer-ical results has shown that the column size is a key designparameter. Long columns appropriate to obtain low IP PERwhen the duration of the fade events caused by power archesis large (e.g., when the train is moving slowly) or when veryspectrally efficient MODCODs are used; but this comes atthe price of a large encoding and decoding delay, and an in-creased sensitivity to random BBFRAME errors caused bynoise and interference. Therefore, the column size must beselected as the result of a tradeoff between competing goals;

it is not possible to propose a single value appropriate forall scenarios. We consider that the column size must be anadaptive parameter, which is changed in response to vari-ations of the propagation conditions, train speed, and soforth. This adaptation would constitute an example of cross-layer optimization, whereby a link layer parameter (i.e., thecolumn size of the FEC matrix) is adapted as function ofthe physical-layer conditions. The padding and puncturingof columns in the FEC matrix are other degrees of freedomthat can be exploited in the parameterization of GSE-FEC.A detailed analysis of these aspects is a subject for furtherresearch.

6.3. Comparative analysis

As it can be seen from the results presented in the last twosections, very satisfactory results to ensure reliable receptioncan be obtained with both techniques. In the case of antennadiversity, this does not penalize the overall system efficiency,although some additional complexity in the receiver imple-menting the MRC scheme will be accounted for. However,the main issue to be addressed in the practice is representedby the installation of two antennas. Many experiments andtrials have shown that this is a very critical point, since anten-nas suitable for installation on trains are subject to very strictrequirements in terms of pointing accuracy, size, and ro-bustness against mechanical vibrations, wind, pressure gra-dients when entering or exiting a tunnel, and so forth. Withcurrent antenna technologies, a relatively high failure rate


Table 2: Parameters of the GSE-FEC algorithm.

FEC-matrix columnsize (bytes)

256 512 768 1024 2048 3072 4096 5120

GSE units per column 1 1 1 2 2 3 4 5

of mechanical components included in the antenna plat-form has to be expected. Furthermore, train operators areextremely keen on keeping the installation and maintenanceprocedures as simple as possible. For all these reasons, addi-tional countermeasures must be also investigated as possiblecomplement to the presence of two antennas (e.g., in caseone antenna suddenly breaks and no immediate replacementis possible).

Although it has been shown that the dimensioning ofpacket level FEC is a complex task, that will be carried outfollowing a cross-layer approach, the results presented in theprevious section confirm that also this technique, if properlydesigned, can guarantee reliable reception at the expenses ofa limited increase in the system complexity and overhead.The concrete solution presented in this paper has been es-pecially devised taking into account the architectural con-straints introduced by the latest encapsulation scheme (GSE)currently being proposed for future DVB systems. Clearly,packet level FEC results in a reduction of the overall spectralefficiency of approximately 33% with the adopted RS code,partially compensated by the migration to a more efficientencapsulation scheme such as GSE.

7. CONCLUSIONS

To conclude, two countermeasures are thoroughly analyzedin this paper: antenna diversity and a packet-level forwarderror correction mechanism especially tailored to DVB-S2,named GSE-FEC. Simulations have shown the excellent per-formance of both approaches, while they have complemen-tary features in terms of hardware complexity, delay, andbandwidth efficiency. Generally speaking, the results in thispaper show that effective countermeasures to compensate theimpairments of the railroad satellite channel are possible andcan be integrated into the existing DVB-S2 standard with alimited to moderate impact on the receiver design and on thesystem complexity. In fact, to support antenna diversity, thereceiver structure will be modified as depicted in Figure 4,whereas for packet level FEC a software implementation maybe considered.

Further topics to be addressed in order to conclude theanalysis of the forward link are the following:

(i) cross-layer optimization of all the relevant parameters(MODCODs and GSE-FEC), taking also into accountnLOS channel conditions and the usage of ACM tocompensate for slower fades due to atmospherical ef-fects,

(ii) inclusion of mechanizm(s) to support QoS and studyof their integration and interaction with the proposedGSE-FEC scheme.

ACKNOWLEDGMENT

This work was supported and partially funded by Sat-NEx, the Satellite Communications Network of Excellence(www.satnex.org), FP6 Contract IST-507052.

REFERENCES

[1] EN 300 421 v1.1.2: Digital Video Broadcasting (DVB); Fram-ing structure, channel coding and modulation for 11/12 GHzsatellite services.

[2] ETSI EN 302 307 v1.1.1: Digital Video Broadcasting (DVB):Second generation framing structure, channel coding andmodulation system for Broadcasting, Interactive Services,News Gathering and other broadband satellite applications.

[3] ETSI EN 301 790 v1.4.1: Digital Video Broadcasting (DVB):Interaction channel for satellite distribution systems.

[4] ETSI TR 101 790 v1.3.1: Digital Video Broadcasting (DVB):Interaction channel for satellite distribution systems; Guide-lines for the use of EN 301 790.

[5] ETSI EN 302 304 v1.1.1: Digital Video Broadcasting (DVB);Transmission System for Handheld Terminals (DVB-H).

[6] S. Scalise, R. Mura, and V. Mignone, “Air interfaces for satellitebased digital TV broadcasting in the Railway environment,”IEEE Transactions on Broadcasting, vol. 52, no. 2, pp. 158–166,2006.

[7] E. Lutz, M. Werner, and A. Jahn, Satellite Systems for Per-sonal and Broadband Communications, Springer, New York,NY, USA, 2000.

[8] S. Scalise, H. Ernst, and G. Harles, “Measurement and mod-elling of the land mobile satellite channel at Ku-band,” to ap-pear in IEEE Transactions on Vehicular Technology.

[9] E. Kubista, F. P. Fontan, M. A. V. Castro, S. Buonomo,B. R. Arbesser-Rastburg, and J. P. V. Polares Baptista, “Ka-band propagation measurements and statistics for land mobilesatellite applications,” IEEE Transactions on Vehicular Technol-ogy, vol. 49, no. 3, pp. 973–983, 2000.

[10] A. Benarroch and L. Mercader, “Signal statistics obtained forma LMSS experiment in Europe with the MARECS satellite,”IEEE Transactions on Communications, vol. 42, no. 2–4, pp.1264–1269, 1994.

[11] G. Sciascia, S. Scalise, H. Ernst, and R. Mura, “Statistical char-acterization of the railroad satellite channel at Ku-band,” inProceedings of the International Workshop of Cost Actions 272and 280, Noordwijk, The Netherlands, May 2003.

[12] S. Scalise, O. Lucke, and E. V. Torralbo, “A link availabilitychannel model for the railroad satellite channel,” in Proceed-ings of 24th AIAA International Communications Satellite Sys-tems Conference (ICSSC ’06), vol. 1, pp. 305–317, San Diego,Calif, USA, June 2006.

[13] S. Cioni, G. E. Corazza, and A. Vanelli-Coralli, “Antenna di-versity for DVB-S2 mobile services in Railway environments,”to appear in Journal of Satellite Communications and Networks,special issue on ASMS Conference.

[14] S. Cioni, M. Berdondini, G. E. Corazza, and A. Vanelli-Coralli,“Antenna diversity for DVB-S2 mobile services in Railway en-vironments,” in Proceedings of the 3rd Advanced Satellite MobileSystems (ASMS) Conference, Herrsching am Ammersee, Ger-many, May 2006.

[15] S. Cioni, A. Vanelli-Coralli, C. Parraga Niebla, S. Scalise, G.Seco Granados, and M.A. Vazquez Castro, “Antenna diver-sity and GSE-based packet level FEC for DVB-S2 systemsin Railway scenarios,” in Proceedings 25th AIAA International


Communications Satellite Systems Conference, Seoul, South Ko-rea, April 2007.

[16] ETSI TR 102 377 v1.2.1: Digital Video Broadcasting (DVB);DVB-H Implementation Guidelines.

[17] DVB Blue Book A116 - Generic Stream EncapsulationSpecification. http://www.dvb.org/technology/bluebooks/a116.tm3762r1.gbs0436r10.GSE spec.pdf.

[18] P. Salmi, M. Neri, and G. E. Corazza, “Design and perfor-mance of predistortion techniques in Ka-band satellite net-works,” in Proceedings of the 22nd AIAA International Commu-nications Satellite Systems Conference and Exhibit (ICSSC ’04),vol. 1, pp. 281–291, Monterey, Calif, USA, May 2004.


Research ArticleCapacity Versus Bit Error Rate Trade-Off inthe DVB-S2 Forward Link

Matteo Berioli, Christian Kissling, and Remi Lapeyre

German Aerospace Center (DLR), Institute of Communications and Navigation, Oberpfaffenhofen, 82234 Wessling, Germany

Received 5 October 2006; Accepted 12 March 2007


The paper presents an approach to optimize the use of satellite capacity in DVB-S2 forward links. By reducing the so-called safetymargins, in the adaptive coding and modulation technique, it is possible to increase the spectral efficiency at expenses of anincreased BER on the transmission. The work shows how a system can be tuned to operate at different degrees of this trade-off,and also the performance which can be achieved in terms of BER/PER, spectral efficiency, and interarrival, duration, strength ofthe error bursts. The paper also describes how a Markov chain can be used to model the ModCod transitions in a DVB-S2 system,and it presents results for the calculation of the transition probabilities in two cases.

Copyright © 2007 Matteo Berioli et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1. INTRODUCTION

The original DVB-S standard dates back to 1995 and was in-tended for delivery of broadcasting services, the underlyingtransport stream of DVB-S was defined to be MPEG-2. DVB-S2 [1] is the second generation of the DVB-S standard andcomprises a variety of new features. It can be used for provi-sion of HDTV (high definition television) but it also allowsfor transportation of different multimedia streams such as,for example, internet traffic, audio and video streaming andfile transfers with support of different input stream formatssuch as IP, ATM, single/multiple MPEG streams or genericbit streams, both for broadcast and unicast transmissions.For the support of interactive applications a return channelis necessary which can be provided by DVB-RCS [2]. DVB-S2 can achieve a capacity increase of up to 30% under thesame transmission conditions compared to the older DVB-Sstandard what is achieved by applying higher order modu-lation schemes and by the use of low density parity checkcodes (LDPC) and Bose-Chaudhuri-Hochquenghem (BCH)codes.

The real novelty introduced by DVB-S2 was the pos-sibility to use adaptive coding and modulation (ACM). Intraditional nonadaptive systems the link dimensioning hasto be made under considerations of service availability andworst case channel assumptions due to the deep fades causedby atmospheric effects; as a consequence the classical fade

mitigation techniques like power control result in an inef-ficient use of the system capacity since most of the time moretransponder power than necessary is used. On the other handin case of ACM, if a terminal is able to inform the gateway ofits particular channel conditions (by means of a proper re-turn link) the gateway can select an appropriate waveform,coding and modulation, to best exploit the spectrum and atthe same time to overcome the channel impairments.

An efficient exploitation of the expensive satellite capac-ity has always been a key factor in the development of thesatellite market, and the improvements brought by DVB-S2give promising perspectives for the future of satellite commu-nications. Nevertheless it is important to keep improving theexploitation of the satellite bandwidth, in order to guaran-tee reduced costs for all satellite services (broadcast, Internet,etc.). The aim of this work is to go one step further in thistrend and to try to optimize the throughput and the spec-trum efficiency in DVB-S2 forward links.

Today DVB-S2 links offer to the higher-layers protocolsa terrestrial-like transmission medium, with recommendedPERs around 10−7. This is of course an excellent result, butnot all services at higher layers require to reach such out-standing performance. This is in particular true for Internetand multimedia services [3].

Some audio codecs (e.g., AMR [4]) can typically accom-modate packet losses with only a small impact in quality, andup to 15% failures before the speech is severely degraded.


Other modern media codecs (e.g., MPEG-4 [5]) have beendesigned to be highly resilient to residual errors in the in-put bit-stream, to detect and localize errors within the packetpayload, and to employ concealment techniques, like for in-stance interframe interpolation, that hide errors from a hu-man user. These codecs offer acceptable quality at a resid-ual BER poorer than 10−3, and some at poorer than 10−2

[6]. In order to support these error-tolerant codecs, the IETFhas also standardized a new multimedia transport proto-col, UDP-Lite [7], that allows to specify the required level ofpayload protection, while maintaining end-to-end deliverychecks (verification of intended destination, IP header fieldsand overall length).

When these services are operating over the satellite con-nection, it is convenient to reduce the quality of the trans-mission in DVB-S2 forward links, by allowing higher BERs,in order to increase the precious capacity and the through-put. The first motivation for this is to make use of cross-layermechanisms by voluntarily allowing higher bit error rateswhich can be compensated with error correction at higherlayers. A second motivation to allow for higher BERs is thatnot all applications have the same stringent BER require-ments. This represents a natural trade-off between errors andcapacity. The present work analyzes this trade-off, proposesa way to tune the system parameters in order to work inoptimal conditions, and investigates the performance of thesystem in this situation. The work is organized as follows:Section 2 presents the background and the scenario of thesubject, Section 3 describes the main ideas of the paper andthe original approach to the problem, Section 4 evaluates theperformance of a system operating in the suggested condi-tions, and Section 5 drives the conclusions of the paper.

2. BACKGROUND AND SCENARIO

2.1. Overview of DVB-S2

The second generation of DVB-S provides a new way of fademitigation by means of adaptation of the coding and modu-lation (ACM) to the different channel states. This of courseimplies the need for every terminal to signal its perceivedchannel state back to the gateway which can then make aframe-by-frame decision of the modulation and coding com-bination (ModCod) to be applied based on these measure-ments. DVB-S2 offers a broad range of modulations and cod-ings for ACM. The supported modulation schemes compriseQPSK, 8-PSK, 16-APSK, 32-APSK and considered codingrates are 1/4, 3/4, 1/3, 2/5, 3/5, 4/5, 1/2, 5/6, 8/9, 9/10. Thepossibility to select the modulation and coding for an indi-vidual destination allows to make a more efficient use of thesystem capacity since transmission in a higher-order modu-lation in combination with a low coding rate (e.g., for clearsky conditions) allows to transmit more bits per symbol thana low-order modulation with high coding rate (e.g., for rainychannels). In this way it is possible to use individually for ev-ery ground terminal (or for every group of terminals in thesame spot beam) the highest possible modulation schemeand the lowest coding rate which still allows to cope with

the channel impairments to provide low BER. A destinationwith a bad channel state can thus use a very robust modula-tion and coding pair (ModCod) while other terminals with avery good channel state can still transmit in highly efficientModCods. The adaptive selection of the best suited ModCodresults in an increased net data throughput while terminalsin bad channel conditions are still able to receive their datasince they can use ModCods with lower-order modulationand higher coding (but at the cost of lower spectral efficiencyand thus lower throughput).

As can be seen in Figure 1 the system architecture ofDVB-S2 is subdivided into six main components [1]. Themode adaptation subsystem provides an interface to the ap-plication specific data stream formats and also contains aCRC-8 error detection coding scheme. It is possible to mergedifferent input streams together and to segment them intothe so-called data fields which are the payload part of the so-called baseband-frames (BBFRAME) created at the outputof the consecutive stream adaptation module. Buffers storedata until they are processed by the merger/slicer and in casenot enough data is available to fill a data field or if it is re-quired to have only an integer number of packets in a frame(in general integer number of packets will not perfectly fitinto a frame but their payload sum will always be slightlysmaller or larger than the data field), the unused space can bepadded, this operation is accomplished by the stream adap-tation subsystem. In order to complete the baseband frame(BBFRAME) additional header information (BBHEADER)is added in front of the data field and scrambling of headerand payload is applied. The final BBFRAME structure is il-lustrated in Figure 2.

The consecutive FEC encoding block performs outer andinner coding and bit interleaving. The coding scheme whichis used is selected based on the channel measurements re-ceived from the terminals the data of which is contained inthe frame. The outcome of this module, called forward errorcorrection frame (FECFRAME), is shown in Figure 3. TheFECFRAMEs can either have a length of 16200 bits for shortframes or 64800 bits for normal frames. Since the lengthof the encoded frame is fixed, this means that the lengthof the payload in the underlying BBFRAME changes withthe applied coding. For applying higher-order modulationschemes the subsequent mapping block performs a serial-to-parallel conversion. The mapper chooses the applied mod-ulation schemes again based on the channel measurementsfor the destination(s) of the data contained in the frame. Theoutcome of the mapping of the data into symbols is calledan XFECFRAME which is afterwards formed into a physicallayer frame (PLFRAME) after pilots and PL signalling havebeen inserted and after final scrambling for optimization ofenergy dispersal. In case no XFECFRAMES are provided bythe preceding subsystems, the PLFRAMING module insertsthe so-called DUMMY PLFRAMES to provide a continuousTDM stream on the link. To allow every terminal indepen-dent of its channel state to receive the PLHEADER informa-tion (which also contains the used modulation and codingscheme for the underlying frame) this header is always mod-ulated with BPSK.

Matteo Berioli et al. 3

Singleinput

stream

Multipleinput

streams

Input

interfaceInput streamsynchroniser

Null-packetdeletion

(ACM, TS)

CRC-8encoder Buffer

BBsignalling

Merger

slicer

BufferCRC-8encoder

Null-packet

deletion(ACM, TS)

Input stream

synchroniser

Input

interface

Data

ACMcommand

Mode adaptation

Dotted subsystems are

not relevant forsingle transport stream

broadcasting

applications

PadderBB

scramBLER

Streamadaptation

Rates 1/4, 1/3, 2/51/2, 3/5, 2/3, 3/4, 4/5,

5/6, 8/9, 9/10

BCHencoder

(nbch, kbch)

LDPCencoder

(nldpc, kldpc)

Bitinter-leaver

FEC encoding

QPSK,8PSK,

16APSK,32APSK

Bitmapper

intoconstellations

Mapping

I

Q

PL signalling &

pilot insertion

PLscramBLER

Dummy

PLFRAMEinsertion

PLFRAMING

α = 0.35, 0.25, 0.2

BB filterand

quadrature

modulation

Modulation

BBHEADERdata field BBFRAME

LP stream forBC modes FECFRAME PLFRAME

To the RFsatellitechannel

Figure 1: DVB-S2 system architecture [1].

80 bits DFL Kbch-DFL-80

BBHEADER Data field Padding

BBFRAME (Kbch bits)

Figure 2: Structure of a BBFRAME [1].

Nbch = kldpc

Kbch Nbch-Kbch nldpc-kldpc

BBFRAME BCHFEC LDPCFEC

(nldpc bits)

Figure 3: Structure of a FECFRAME [1].

For the selection of a ModCod that is adapting to the in-dividual experienced channel states of the terminals, a returnlink must be provided to give feedback information aboutthe measured channel states to the gateway. The gateway canthen use this information to select a ModCod that suits trans-missions in this channel state. This means the ModCod isselected to provide a quasi-error-free transmission as long asthe critical SNR (signal-to-noise ratio) demodulation thresh-old for this ModCod (thrdem (ModCod)) is not crossed. If thesignal drops below thrdem (ModCod) then the BER will dras-tically increase due to the nature of the applied LDPC andBCH coding of having very steep BER-versus-SNR curves. Inthe GEO-stationary scenario investigated here, the propaga-tion delay of the information feedback from the terminal tothe gateway takes relatively long and it is in the order of sev-

eral hundreds milliseconds (250 milliseconds). This meansthat though the order of magnitude for the propagation de-lay allows for a compensation of very slow changing channeleffects, like rain attenuation, it is too long to compensate fast,high-frequent changes in the SNR as those caused by scintil-lation, this will be explained in the next section.

2.2. Channel modelling

The selection of a ModCod scheme for transmission is verydecisive for the performance of the system in terms of netdata rate, bit errors and, respectively, packet errors. If theModCods are selected too aggressively (meaning selection ofModCods with a too high modulation scheme and a too lowcoding) the transmission will result in a drastically higherPER. On the other hand, selection of safe ModCods (mean-ing a ModCod with a modulation lower than what would benecessary and a coding higher than necessary) will result ininefficiencies which reflects in a lower net data rate. In or-der to evaluate the influence of different parameters for theModCod selection it is important to have a realistic chan-nel model. The channels in satellite systems face mainly twosources of signal fading, rain attenuation and scintillation.The effect of rain attenuation is very significant for systemsoperating in K-band where the signal is attenuated by ab-sorbing effects of the water. The second effect coming alongwith rain attenuation is scintillation which is basically a highfrequent distortion of the signal amplitude and phase causedby small-scale irregularities in electron density in the iono-sphere [8].

The scintillation in K-band can be considered to be a nor-mal distributed random variable with a non linear spectrum(see [9, 10]) as shown in Figure 4. The standard deviation


10110010−110−210−310−4 fsfa

Frequency (Hz)

10−6

10−4

10−2

100

102

104

PSD

(dB

2/H

z)

Power spectral density of rain attenuation and scintillation

Rain attenuationScintillation

∼ f −8/3

∼ f −2

Figure 4: Attenuation and scintillation spectrum (typical values:fa ≈ 10−4 Hz, fs ≈ 0.1− 0.65 Hz).

of the scintillation process can be calculated according to (1)corresponding to the theory of Tatarskii [9] and the model ofMatricciani [10],

σ = σ0 · A5/12. (1)

The value σ0 is the standard deviation of the scintillation fora rain attenuation of A[dB]. [10] suggests a typical value of0.039 for σ0 in the frequency range of 19.77 GHz. Accordingto (1) the resulting scintillation standard deviation σ is thenin the order of tenths of a dB for rain attenuations smallerthan 20 dB.

Within this work the main focus is on the scintillationeffects since these cannot be compensated by signalling ofthe channel states via the return channel because of thelong propagation delay of the GEO satellite. Nevertheless thechannel simulations used in the rest of this work considerspatial correlated rain attenuation as well since the magni-tude of the scintillation also depends on the intensity of therain attenuation (see (1)). Similar to the generation of thescintillation, also the rain attenuation is created via a normaldistributed random variable whereas its spectrum has a dif-ferent corner frequency of fa (see also Figure 4).

Figure 5 shows a channel example for the attenuationcaused by scintillation and rain for a user located at longi-tude 8.6◦E and latitude 52.7◦N, in the area around Hamburg(Germany). It can be seen here that scintillation effects occurwith a much higher frequency than regular rain attenuationevents and how rain attenuation and scintillation are corre-lated.

2.3. ModCod switching strategies

While the rain attenuation occurs on a larger time scale scin-tillation effects occur very rapidly. For this reason rain fad-

800070006000500040003000200010000

Time (s)

−0.25

−0.2

−0.15

−0.1

−0.05

0

0.05

0.1

0.15

0.2

0.25

Scin

tilla

tion

(dB

)

Scintillation and attenuation time seriesof useful user (forward downlink)

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Att

enu

atio

n(d

B)

Figure 5: Example of scintillation and rain attenuation.

ing can be mitigated by mode adaptation whereas counter-measures for scintillation require a different compensation.For every combination of modulation and coding a thresholdthrdem (ModCod) exists which is needed to be able to decodethe frame with a quasi-zero BER. The decision of the gatewayon which ModCod will be used is thus driven by thresholds.For switching among ModCods these thresholds could theo-retically be used directly for the decision about which Mod-Cod will be used, but in practice this would result in frequenttransmission errors since the high frequent variations of thechannel (due to scintillation) would cause a frequent crossingof the threshold. On the one hand, this high frequent cross-ing cannot be compensated by signalling to the gateway, onthe other hand such signalling would also mean a high fre-quent change of the ModCod which is as well undesirable.

To provide more reliability the minimal needed demod-ulation thresholds thrdem (ModCod) can be replaced bythresholds which have a certain safety margin. This meansthat a lower ModCod is selected already before the criticalthreshold (the threshold below which a strong increase inbit error rate occurs) is reached. The size of the safety mar-gin does thus determine the robustness against fast occurringscintillation fades. On the other hand, this size of the safetymargin also influences the system performance since trans-mission in a higher ModCod would result in a higher netdata rate. Since fast oscillations between neighboring Mod-Cods are also possible when safety margins are used, an ad-ditional hysteresis margin is introduced. Figure 6 illustratesthe different thresholds and margins.

Within Figure 6 the terms thrdem(N − 1) and thrdem(N)denote the minimum SNR values which are just enough toprovide quasi error free decoding. If, for example, ModCodN is used and the signal strength falls below the thrdem(N)threshold, the BER will drastically increase. These thresholdshave also been called critical in [11] for this reason. If on theother hand the signal strength increases, for example, whileusing ModCod N−1, the next higher ModCod is not selectedas soon as the demodulation threshold of the next higher


ModCod (thrdem(N) in this case) is crossed but after a higherthreshold is exceeded (threnable(N − 1)).

In case the signal strength decreases again, the ModCod isnot switched when the enabling threshold threnable is crossed,but just when an additional hysteresis margin is exceeded.The threshold for switching to a smaller ModCod is denotedas thrdown (ModCod) and the size of the hysteresis margin as(Δthrhyst(N)). The distance between the critical demodula-tion threshold thrdem (ModCod) and the threshold that trig-gers a downswitching thrdown (ModCod) is called the safetymargin Δthrsafety (ModCod).

The safety margin(Δthrsafety (ModCod)) can be seen asan additional security for high frequent oscillations whichcannot be countervailed due to the long satellite propagationdelay. If the signal strength oscillates within this area no in-crease in BER will occur since the thrdem (ModCod) thresh-old is not crossed. The values for the safety margin and thehysteresis margin can be varied and they can also be differentfor every ModCod. Worz et al. [11] presented a calculationmethod for all aforementioned parameters which provides aquasi error free system performance. The calculation of theparameters in [11] mainly depends on estimated values ofthe scintillation standard deviations and a numerically de-rived function which accounts for the fact that the standarddeviation of the scintillation is also dependent on the inten-sity of the rain attenuation.

Within the remaining parts of this work the influence ofthe size of the safety margins with respect to gain or loss inchannel net efficiency and increase/decrease of BER is inves-tigated. The term “Worz-Schweikert safety margins” denotesthe safety margins calculated according to the algorithm pre-sented in [11] while “zero-safety margin” denotes the factthat no safety margin is used.

2.4. Investigated environment

Within the examined scenarios, a set of user terminals hasbeen located in a geographical region close to the city ofHamburg, Germany (longitude 9.5◦−10.5◦E, latitude 52.5◦−54◦N) within the aforementioned channel simulator. The setcomprises 38 different terminal locations whereby the chan-nel states are sampled with 10 Hz. The investigated durationis 7200 seconds per simulation run. In order to get statisticalsignificant results the simulation duration of 7200 secondsper simulation have been extended to 60 hours. The 60 hourschannel simulation results for the 38 terminals can be seen as2280 hours of simulated channel states for a single terminalwhat in turn means that all results are based on channel in-formation which corresponds to roughly a quarter of a year.

3. SYSTEM MODELLING

The main idea behind this study is that by reducing the safetymargin in the ModCod switching strategy it is possible togain in spectral efficiency, and thus to increase the net datathroughput, at the expenses of an increased BER (and con-sequently a higher PER). In order to investigate this and toderive a detailed quantitative estimation of this trade-off, it

ModCod N − 1 ModCod N

threnable(N − 1)

thrdown(N − 1)

Δthrsafety(N − 1)

thrdem(N − 1)

Δthrhyst(N)

Δthrsafety(N)

No switchinghere becauseof hysteresis

Signal

thrdown(N)

thrdem(N)

Time

SNIR

Figure 6: Illustration on the different thresholds.

is important to carefully describe the assumptions on whichthe analysis is based, this is what is presented in this sec-tion. Though the obtained results have a quantitative mean-ing only considering these assumptions, it is worth statingthat their qualitative relevance has a general importance, as itwill be later explained.

Existing systems compliant with the DVB-S2 standardcan provide the higher-layers protocols with a quasi-error-free underlaying physical layer (PER = 10−7). For this pur-pose regular 8-bytes CRC (cyclic redundancy check) fieldsare used to identify errors in the BBFRAME, which were notcorrected by the coding schemes (LDPC and BCH) at re-ception. In case an error is detected in a frame, it has to beconsidered that the wrong bit(s) cannot be singularly identi-fied in the frame, so one of the two following choices can bemade:

(1) the whole frame is discarded (this is what is normallydone);

(2) the packets in the frame are passed to the higher proto-cols with uncorrected failures (this can be done in casethe higher protocols are able to cope with errors).

These cases are very rare when high safety margins areadopted, and systems are normally dimensioned to avoidthem, but they become more frequent if the system workscloser to the demodulation thresholds (as we defined themin the previous section), for the reasons already explained.

If a system is dimensioned also to operate in these con-ditions, it is important to evaluate the statistical propertiesand characteristics of these situations, that is, how often theyoccur and what failures they bring in comparison to the ca-pacity gain. In order to do that we performed three levelsof analysis. They are theoretically described in this sections,whereas the results obtained for each of them are shown anddiscussed in the next one.

3.1. Markov model

The first analysis is a comparison of the new approach witha classical one existing in literature (the already mentionedWorz et al. [11]), in terms of ModCod switching statistics.


The best way to show the difference between the two ap-proaches is to model the system according to a Markov chain,where each state represents the system operating with oneparticular ModCod. The chain presents two states for eachModCod N : the good one, NG, and the bad one, NB; so theoverall number of states is twice the total amount of allowedModCods (56). In the good state the SNR measured at the re-ceiver is above the demodulating threshold for that ModCod,and so no failures are expected, in the bad state the systemSNR is below the demodulating threshold for that ModCod,and so failures may occur with probabilities that are not neg-ligible.

A similar Markov chain is an excellent model, because itsummarizes very well the properties of a ModCod switch-ing approach. So once the transition probabilities for oneparticular ModCod switching criterion have been calculated(normally by simulations), the Markov chain can be usedas a basis for all types of analysis without the need of run-ning again computationally heavy simulations, which mightbe very long in order to gather statistically meaningful data.In this sense the calculated Markov chain (i.e., the ModCodtransition probabilities) can be considered independent fromthe simulated channel conditions, only if the simulation islong enough to represent general channel statistics. On theother hand, it should be mentioned that the same Markovchain depends on some parameters which might be charac-teristic of particular cases, for example, the link budget inclear sky, and consequently the system availability. So even ifthe resulting numbers are only meaningful bearing in mindthese assumptions, the quantitative conclusions which can bederived have general relevance, and this will be clearer in thenext section.

3.2. Error rate versus capacity trade-off

The second level of analysis describes the details of each stateof the Markov chain. The good states present quasi-error-freeconditions according to the DVB-S2 recommendations, soPER = 10−7. Since the BER versus SNR characteristics forall ModCods are very steep, the BER values increase quiterapidly when the SNR level goes below the demodulatingthreshold. In particular they change of several orders of mag-nitude within a few tenths of dB, going from BER ≈ 10−10

when SNR is close or bigger than the demodulating thresh-olds, up to BER ≈ 10−2 when the SNR is just 0.3 dB be-low the threshold. Each bad state represents a set of differentBERs, the proper BER is selected at each time step accordingto the received level of SNR with respect to the demodulat-ing thresholds. The exact characteristics for the BER-versus-SNR functions, which were used in the simulations and toderive the Markov chain parameters, were taken from [12].In that work, end-to-end performances of the BER versusthe SNR are presented for the DVB-S2 system, the wholecommunication chain is modelled and simulated, includingcoding, modulation with predistortion techniques, satellitetransponder impairments, downlink, demodulation with thesynchronization, and the final LDPC and BCH decoders. Inthe Markov chain, each ModCod might have its own BER

versus SNR characteristic, but to use one single function forall ModCods already seems an excellent approximation to thereal case, so this is how it was implemented in the simulator.

PERs are derived from these BERs under considerationof the payload length of each BBFRAME also regarding theapplied ModCod. A BBFRAME is considered as erroneous ifat least one of the payload bits is erroneous. For the rest ofthis paper the term PER denotes the BBFRAME packet errorrate. Thanks to this definition of the states of Markov chain,this model allows to derive the properties of the communi-cation in terms of PER and BER statistics, and by knowingthe spectral efficiency associated to each ModCod it is easy toderive an average resulting capacity.

3.3. Error bursts analysis

The third and last level of analysis goes into the details of thefailures introduced with this novel approach. In the previoussection we explained how to derive a measure of the trade-off between average capacity and average BER (or PER). Anaverage measure of the BER (or PER) does not seem a veryprecise information, since these failures come in bursts. Theerrors are mainly due to the ModCod switchings, and theyare mostly introduced by reduced safety margins. So we wantto investigate three main properties: (i) how often the errorbursts arrive (interarrival times statistics), (ii) how long thebursts last (duration statistics), and (iii) how deep the fadesare (i.e., how high are BER and PER during one error burst).These three properties can be estimated thanks to the Markovmodel, and this analysis produces interesting information,which will be presented in the next section.

4. RESULTS EVALUATION

4.1. Markov model

A software simulator was developed in order to derive theMarkov model presented in the previous section. Once theModCod switching criterion has been specified the softwaresimulates the evolution over time of the system; from thesesimulations we can derive statistics about the permanence inthe different ModCods for each ModCod switching criterion,this was done by computing transition matrices and solvingthem. In the following we present two full transition matricesfor two different ModCod switching criteria.

Simulations equivalent to 3 months of SNR time serieshave been carried out, one using Worz-Schweikert safetymargins, the other one using zero-safety margin bounds withWorz-Schweikert hysteresis bounds.

The matrices in Figures 7 and 8 represent the transitionprobabilities for those two approaches, where position (i, j)is the probability in each time step (0.1 second) to move fromstate i to state j; the first line and the first column of eachModCod represent the bad state (iB and jB), the second onethe good state (iG and jG). Figures 7 and 8 show the transi-tion matrices for zero-safety margin and the Worz-Schweikertsafety margins. The cells marked black indicate that theircontent is unequal to zero. In Figure 8, we can see that the


1 2 3 4 5 6 7 8 9

1, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00

1 0, 01 0,99 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00

0, 00 0,13 0, 74 0,13 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00

2 0, 00 0,00 0, 00 0,99 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00

0, 00 0,00 0, 00 0,14 0, 74 0,12 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00

3 0, 00 0,00 0, 00 0,00 0, 00 0,99 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00

0, 00 0,00 0, 00 0,00 0, 00 0,14 0, 73 0,13 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00

4 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,99 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00

0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,14 0, 72 0,14 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00

5 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,99 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00

0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,13 0, 71 0,16 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00

6 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 1,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00

0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,13 0, 71 0,16 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00

7 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,99 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00

0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,12 0, 71 0,16 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00

8 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,99 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00

0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,13 0, 71 0,17 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00

9 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,99 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00

0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 01 0,12 0, 73 0,15 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00

12 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 1,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00

0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,12 0, 70 0,18 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00

11 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,99 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00

0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 01 0,11 0, 71 0,17 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00

13 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 1,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00

0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,11 0, 70 0,19 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00

14 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 1,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00

0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,10 0, 66 0,23 0, 00 0,00 0, 00 0,00 0, 00 0,00

18 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 1,00 0, 00 0,00 0, 00 0,00 0, 00 0,00

0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,09 0, 65 0,26 0, 00 0,00 0, 00 0,00

19 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 1,00 0, 00 0,00 0, 00 0,00

0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,07 0, 57 0,36 0, 00 0,00

20 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 1,00 0, 00 0,00

0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,07 0, 57 0,37

21 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 1,00

12 11 13 14 18 19 20 21

Figure 7: Transition matrix for zero-safety margin.

1 2 3 4 5 6 7 8 9

1, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00

1 0, 01 0,99 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00

0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0 ,00 0 ,0 0

2 0, 00 0,00 0, 00 0,99 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00

0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0 ,00 0 ,0 0

3 0, 00 0,00 0, 00 0,00 0, 00 0,99 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00

0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0 ,00 0 ,0 0

4 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 1,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00

0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0 ,00 0 ,0 0

5 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,99 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00

0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0 ,00 0 ,0 0

6 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 1,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00

0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0 ,00 0 ,0 0

7 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,99 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00

0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0 ,00 0 ,0 0

8 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,99 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00

0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0 ,00 0 ,0 0

9 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,99 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00

0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0 ,00 0 ,0 0

12 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 1,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00

0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0 ,00 0 ,0 0

11 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,99 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00

0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0 ,00 0 ,0 0

13 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 1,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00

0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0 ,00 0 ,0 0

14 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 1,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00

0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0 ,00 0 ,0 0

18 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 1,00 0, 00 0,00 0, 00 0,00 0, 00 0,00

0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0 ,00 0 ,0 0

19 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 1,00 0, 00 0,00 0, 00 0,00

0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0 ,00 0 ,0 0

20 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 1,00 0, 00 0,00

0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0 ,00 0 ,0 0

21 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,00 0, 00 0,01 0, 00 0,99

18 19 20 2112 11 13 14

Figure 8: Transition matrix for Worz-Schweikert safety margin.

more “stable” states are the good states. This makes sense ifwe look at the SNR time series, because switchings betweenModCods are quite spaced in time compared to the time stepof 0.1 second. Simulations estimate an average number of 4.5ModCod switchings per hour.

Moreover on the diagonal, the probabilities of remainingin a bad state are not so high; this is also correct, since whenwe are in a bad state, we know that a down-switch shouldoccur. The only bad state which has a higher stability is thebad state for ModCod 1B. This results from the fact that whenthe SNR goes below the last demodulation threshold, the sys-tem cannot switch to a lower ModCod, so it remains in badstate until the SNR rises again. This is basically an outagewhere the DVB-S2 receiver is not available; the simulator wasdesigned to give a system availability of 99.96% of the time,for both approaches.

With the Worz-Schweikert scheme, shown in Figure 8, thematrix is far more sparse, and no bad states are ever ac-tive, except for ModCod 1B because of system unavailabil-

ity. Transitions only occur between good states and this con-firms that this approach is designed to work only in goodstates.

For the novel approach, the zero-safety margin one, itmay be interesting to derive the probability to be in eachModCod (bad or good state). Once the transition matrixfor the Zero-Safety margin is solved [13], we end up withFigure 9 which shows a stacked probability density graph forgood and bad states of each ModCod. This is the result ofa simulation of an equivalent of 4.5 years of SNR evolutionover time. What we can see is that the most used ModCodsare those whose demodulation threshold is just below theSNIR in clear sky conditions. That makes sense because mostof the time we are in clear sky conditions, so we use the high-est ModCods. We can also notice the high value of the badstate in ModCod 1B, because of system unavailability. SomeModCods are never used due to overlapping with other ones,some ModCods achieve a better spectral efficiency requiringless SNR.


282624222018161412108642

ModCods

10−6

10−5

10−4

10−3

10−2

10−1

100

Pro

babi

lity

Bad statesGood states

Figure 9: State probabilities.

4.2. Error rate versus capacity trade-off

This section presents the main results which are obtainedwhen reducing the safety margins, in terms of increase spec-tral efficiency and increase errors. The starting point is the setof threshold selected by Worz-Schweikert; this set guaranteesa quasi-error-free system operation. We try to proportionallyreduce those margins and even to have negative margins, tosee how the system performs. The x axis in Figures 10 and 11represents factors to be multiplied to the Worz-Schweikertset to get the tested thresholds. This means that for multiply-ing factor 1 we have the Worz-Schweikert set, for the factor0, we have the zero-safety margin approach, and for negativevalues of the factors we are testing thresholds which are be-low those thresholds recommended by the DVB-S2 standard.This may seem strange, but it will appear clear how usefulthis is to show that there is a trade-off between errors andincrease in capacity.

Figure 10 shows (as expected) that the PER objective of10−7 is achieved already before the Worz-Schweikert bounds.This is not surprising since the model has been designed todo so. As expected as well, PER and BER are fast-growing upto 1 when the safety margin becomes negative. A surprisingfact here is that there are possibilities to achieve the goal PEReven for margins which are 0.4 times the Worz-Schweikertsafety margins. That means that those Worz-Schweikert mar-gins may not be the optimum selection.

Figure 11 shows the core result of this work. A trivialthing is that the gross capacity (total amount of received bitswith failures) is still increasing when we go for lower andlower bounds, because of course we are using less and lessrobust ModCods that provide better spectral efficiency. Thevery interesting point comes with the fact that the net ca-pacity (throughput of correct bits) shows a maximum in thenegative part of the scaling factor: −0.4 at the packet level

0.50−0.5−1−1.5−2−2.5−3

Multiplying factor on Schweikert-Worz safety margin

10−10

10−9

10−8

10−7

10−6

10−5

10−4

10−3

10−2

10−1

100

Err

orra

te

Packet error rateBit error rate

6× 10−34× 10−3

Figure 10: Packet error rate (PER) versus Safety margin.

10.50−0.5−1−1.5−2−2.5−3

Multiplying factor on Schweikert-Worz safety margin

0

0.5

1

1.5

2

2.5

3

3.5

Ave

rage

spec

tral

effici

ency

(b/s

/Hz)

Max @− 1.5 = 3.12 b/Hz/s Max @− 0.4 = 3.01 b/Hz/s

Gross efficiencyNet efficiency (without bit aggregation)Net efficiency (with bit aggregation)

Figure 11: Average spectral efficiency versus safety margin.

and −1.5 at the bit level. Corresponding values of PER/BERat these maxima are 6 · 10−3 and 4 · 10−3. The two curvesrepresent the two ways of operating described in Section 3:bit aggregation is when failures cause BBFRAME discard, nobit aggregation means when the frame is passed to the higherlayers with failures. It should be noted that for bit error ag-gregation (see Figure 11) the PER (see Figure 10) is the rele-vant result since in case of a bit error the complete BBFRAMEis discarded. Without consideration of bit error aggregation,the BER is the relevant result since erroneous bits within theBBFRAME are expected to be corrected by the higher layers.This means that a system which wants to have the indicatedthroughput with or without bit aggregation, is operating atthose PER/BER.


21.91.81.71.61.51.41.31.21.11×104

Time in samples (0.1 s)

3

4

5

6

7

8

9

SNIR

atre

ceiv

eran

dM

odC

odse

lect

ion

10−710−610−510−410−310−210−1100

MP

EG

-2pa

cket

erro

rra

te

Figure 12: PER with SNR and ModCod selection for zero-safetymargin.

55005000450040003500300025002000150010005000

Interarrival time of error bursts (event where PER > 10−6) (s)

10−3

10−2

10−1

100

Pro

babi

lity

Probability density function for interarrival times

Figure 13: Interarrival times distribution.

If a system can cope with these error rates, then it may beinteresting to design it with lower safety margins than thosein the Worz-Schweikert strategy, in order to gain throughput.

4.3. Error bursts analysis

To deeper investigate the quality of the transmission in casewe reduce the safety margins, we have to look at the dis-tribution in time of the error bursts. Figure 12 shows anexample of simulated SNR time series with correspondingPER for zero safety margin. In contrast to Figure 10 whichshows the averaged error PERs and BERs, here we investigatethe distribution of the interarrival times between two PERpeaks (without averaging), considering a detection thresholdof PER = 10−6. The simulation that has led to Figure 13 hasbeen worked out on 4.5 years of simulated SNR, and it wasconducted with the zero-safety margins approach.

> 0.50.50.40.30.20.1Fade duration (s)

1e − 11e − 2

1e − 31e − 4

1e − 51e − 6

PERlevel

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Even

tsp

erh

our

Figure 14: State probabilities.

We see that in 50% of cases, the time between two er-ror bursts is in the range of 0–100 seconds. This distributioncomes from the fact that during a rain fade, ModCods areswitched down one by one, and as we saw on Figure 12, errorpeaks often occur at every down-switch. The question is nowwhat is the duration/severity of these peaks?

Figure 14 shows the number of fade events per hour us-ing zero-safety margins, sorted by their duration and PERstrength. A sequence of samples is considered as one fadeevent if the associated PER is exceeding a given level. Foreach PER level, Figure 14 shows the number of fades per hourwhich exceed this PER level. For this graph, we have 6 dif-ferent PER levels, and the fade events are distributed amongtheir duration. We can see that the shorter fades are the onesthat occur most of the time. This comes from the fact that fora normal process like scintillation, the probability of having afade is decreasing exponentially with its duration. There arepeaks for each PER level at 0.5 second, this is due to the factthat independently from how long the fade would be, in theworst case the system can switch to a lower ModCod withinhalf a second (twice the GEO propagation delay), which isthe time needed to signal to the gateway the fading situationand to receive a new transmission with a new ModCod. Soin theory fade should not exceed 500 milliseconds, but thelast bin of this bar plot shows that even if they are rare, fadesexceeding 0.5 second do exist. There are two explanations forthat. First, if we are in the highest ModCod of a couple of veryclose ModCods (in terms of demodulation threshold) and weenter a strong rain fade, with a steep decreasing SNR, it canhappen that the SNR crosses the demodulation threshold ofthe lowest ModCod before the system has switched down.This results in a bad state to bad state transition, and we cansee some of these cases in the transition matrix (12B to 9B or13B to 11B, e.g.). A second explanation is the following, non-negligible contributions to this behavior are the outages dueto system nonavailability, that is the fades that occur in thelowest ModCod.


5. CONCLUSIONS

The possibility to have a quasi-error-free transmission chan-nel in DVB-S2 systems is not always an optimal solution incase the higher-layer protocols do not require such high per-formance. In this case the lower layers can provide a trans-mission with some resilient errors, and exploit more thespectrum to gain in throughput. The error-capacity trade-offcan be tuned, according to the requirements of each partic-ular system, with the adjustment of the ModCod safety mar-gins. The paper presents the gain in spectral efficiency, whichis obtained with this method, and the statistical characteris-tics of the “artificially” introduced error bursts, in terms ofinterarrival, duration and depth (PER). One additional in-teresting side-outcome of this work is the development ofMarkov chain to model the ModCod transitions and the fail-ure occurrence in a DVB-S2 system.

ACKNOWLEDGMENTS

This work was partly supported by EC funds SatNEx underthe FP6 IST Programme, Grant number: 507052. This workwas supported by the European Satellite Network of Excel-lence (SatNEx).

REFERENCES

[1] ETSI EN 302 307 V1.1.2, “Digital Video Broadcasting (DVB);second generation framing structure, channel coding andmodulation systems for broadcasting, interactive services,news gathering and other broadband satellite applications,”June 2006.

[2] ETSI EN 301 790 V1.4.1, “Digital Video Broadcasting (DVB);interaction channel for satellite distribution systems,” April2005.

[3] G. Fairhurst, M. Berioli, and G. Renker, “Cross-layer controlof adaptive coding and modulation for satellite Internet multi-media,” International Journal of Satellite Communications andNetworking, vol. 24, no. 6, pp. 471–491, 2006.

[4] ETSI TS 126 102, “AMR Speech Codec,” 2001.[5] ISO/IEC 14496-2, “Coding of audio-visual objects (MPEG-

4)—part 2: visual,” 2004.[6] ETSI TR 126 975, “Performance Characterisation of the Adap-

tive Multi-Rate (AMR) Speech Codec,” 2004.[7] L.-A. Larzon, M. Degermark, S. Pink, L.-E. Jonsson, and G.

Fairhurst, “The Lightweight User Datagram Protocol (UDP-Lite),” IETF, RFC 3828, 2004.

[8] S. Datta-Barua, P. H. Doherty, S. H. Delay, T. Dehel, and J.A. Klobuchar, “Ionospheric scintillation effects on single anddual frequency GPS positioning,” in Proceedings of the 16th In-ternational Technical Meeting of the Satellite Division of the In-stitute of Navigation (ION GPS/GNSS ’03), pp. 336–346, Port-land, Ore, USA, September 2003.

[9] V. I. Tatarskii, Wave Propagation in a Turbulent Medium,McGraw-Hill, New York, NY, USA, 1961.

[10] E. Matricciani, M. Mauri, and C. Riva, “Relationship betweenscintillation and rain attenuation at 19.77 GHz,” Radio Science,vol. 31, no. 2, pp. 273–280, 1996.

[11] T. Worz, R. Schweikert, A. Jahn, and R. Rinaldo, “Physicallayer efficiency of satellite DVB using fade mitigation tech-niques,” in Proceedings of the International CommunicationSatellite Systems Conference (ICSSC ’05), Rome, Italy, Septem-ber 2005.

[12] E. Casini, R. De Gaudenzi, and A. Ginesi, “DVB-S2 modemalgorithms design and performance over typical satellite chan-nels,” International Journal of Satellite Communications andNetworking, vol. 22, no. 3, pp. 281–318, 2004.

[13] M. F. Neuts, Matrix-Geometric Solutions in Stochastic Models:An Algorithmic Approach, Dover, Mineola, NY, USA, 1981.


Research ArticleFrequency Estimation in Iterative Interference CancellationApplied to Multibeam Satellite Systems

J. P. Millerioux,1, 2, 3, 4 M. L. Boucheret,2 C. Bazile,3 and A. Ducasse5

1 TeSA, 14-16 Port Saint-Etienne, 31000 Toulouse, France2 Institut de Recherche en Informatique de Toulouse, Ecole Nationale Superieure d’Electrotechnique, d’Electronique,d’Informatique, d’Hydraulique et des Telecommunications, 2 Rue Camichel, BP 7122, 31071 Toulouse, France

3 Centre National d’Etudes Spatiales, 18 Avenue E. Belin, 31401 Toulouse Cedex 4, France4 Ecole Nationale Superieure des Telecommunications, 46 Rue Barrault, 75634 Paris Cedex 13, France5 Alcatel Alenia Space, 26 Avenue J.F. Champollion, BP 1187, 31037 Toulouse, France

Received 31 August 2006; Revised 26 February 2007; Accepted 13 May 2007


This paper deals with interference cancellation techniques to mitigate cochannel interference on the reverse link of multibeamsatellite communication systems. The considered system takes as a starting point the DVB-RCS standard with the use of convolu-tional coding. The considered algorithm consists of an iterative parallel interference cancellation scheme which includes estima-tion of beamforming coefficients. This algorithm is first derived in the case of a symbol asynchronous channel with time-invariantcarrier phases. The aim of this article is then to study possible extensions of this algorithm to the case of frequency offsets af-fecting user terminals. The two main approaches evaluated and discussed here are based on (1) the use of block processing forestimation of beamforming coefficients in order to follow carrier phase variations and (2) the use of single-user frequency offsetestimations.

Copyright © 2007 J. P. Millerioux et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1. INTRODUCTION

Multiuser detection appears as a promising way to mitigatecochannel interference (CCI) on the reverse link of multi-beam satellite systems. It can allow considering more capac-ity efficient frequency reuse strategies than classical systems(in which cochannel interference is assimilated to additivenoise). However, channel estimation appears to be a criti-cal point when performed before multiuser processing. Thispaper proposes a multiuser detection scheme coupled withchannel reestimations.

This study is the continuation of the work reported in[1]. The considered system is inspired by the DVB-RCS stan-dard [2], with the use of convolutional coding. The algorithmis derived for a symbol-asynchronous time-invariant chan-nel [1]. It basically consists of a parallel interference cancel-lation (PIC) scheme which uses hard decisions provided bysingle user Viterbi decoders, and includes channel reestima-tion. The aim of this paper is to propose results on possibleadaptations of this algorithm to the more realistic case of fre-quency offsets affecting user terminals.

Other approaches have been proposed in the literaturewith similar contexts. In [3], an iterative decoding schemeis proposed with a very simplified channel model and with-out considerations on channel estimation issues. In [4, 5],MMSE and noniterative MMSE-SIC schemes are evaluatedin a realistic context and the problem of channel estima-tion before multiuser processing is addressed based on pi-lot symbols. In this paper, we consider a joint multiuserdetection and channel estimation approach, which can no-tably allow reducing the required number of pilot symbols,and consequently lead to more spectrally efficient transmis-sions, in particular for a burst access. Notice however thatthe algorithm considered here is suboptimal. Some poten-tially optimal algorithms have been studied in [1]. However,they have appeared much more complex than the one con-sidered here, and have shown a gain in performance pos-sibly very limited, and highly dependant on the antennaimplementation.

The paper is organized as follows: the system modeland assumptions are described in Section 2, Section 3 intro-duces the algorithm on a time-invariant channel, Section 4 is


Informationbits user k

EncoderQPSK

mapping Πk

Pilotsymbolsinsertion

Tk

dk[n]

(a)

dk[n] s(t − τk)

ρke jϕk(t)

x1(t)

xk(t)

xK (t)

H

nk(t)

yk(t)

(b)

Figure 1: Transmitter and channel model.

dedicated to the study of possible adaptations with frequencyoffsets, and we draw conclusions in Section 5.

2. SYSTEM MODEL AND ASSUMPTIONS

2.1. Model

The considered context is the reverse link of a fixed-satelliteservice with a regenerative geostationary satellite, a multi-beam coverage with a regular frequency reuse pattern [6],and an MF-TDMA access [2]. A “slot synchronous” systemis assumed. Multiuser detection is performed onboard thesatellite, after frequency demultiplexing. We choose here towork on a fictitious interference configuration characterizedby carrier to interference ratios C/I . A more detailed presen-tation can be found in [1] or [7].

We consider in the following a frequency/time slot inthe MF-TDMA frame. Notations are relative to complex en-velops. ·∗, ·T , ·H , E(·), and · ∗ · denote, respectively, theconjugate, transpose, conjugate transpose, expected value,and convolution operators. Consider K uplink signals asso-ciated to K different cochannel cells. Under the narrowbandassumption [8], we get

y(t) = Hx(t) + n(t), (1)

where x(t) = [x1(t) · · · xK (t)]T is the K × 1 vector of re-ceived signals, y(t) = [y1(t) · · · yK (t)]T is the K × 1 vec-tor of signals at the beamformer outputs, H is the K × Kbeamforming matrix (i.e., the product of the matrix of steer-ing vectors by the matrix of beamformer coefficients), andn(t) = [n1(t) · · ·nK (t)]T is the vector of additive noises.Without loss of generality, we consider that the matrix Hhas its diagonal coefficients equal to 1. Additive noises areadditive white Gaussian noises (AWGN) with the same vari-ance σ2, and are characterized by a spatial covariance matrixRn = E(n(t)n(t)H) which depends on the antenna imple-mentation [1].

As regards to the waveform, the information bits are con-volutionally encoded, and the coded bits are then mappedonto QPSK symbols which are interleaved differently on eachbeam. A burst of N symbols dk[n] is composed of these in-terleaved symbols in which pilot symbols are inserted. Wemodel the signals xk(t) as

xk(t) = ρkejϕk(t)

N−1∑

n=0

dk[n]s(t − nT − τk

), (2)

where T , s(t), ρk, ϕk(t), τk, denote, respectively, the symbolduration, the normalized emitter filter response (square rootraised cosine with rolloff equal to 0.35 [2]), the amplitude ofthe kth signal, its (possibly time-varying) carrier phase, andits time delay. The whole transmitter and channel model issummarized in Figure 1. Notice that a single frequency refer-ence is assumed on-board the satellite.

We define the signal-to-noise ratio (SNR) for the kth sig-nal as

EsN0

∣∣∣∣k= ρ2

k

σ2. (3)

Assuming an equal SNR for all users, the carrier to interfer-ence ratio for the kth signal can be simply defined as

C

I

∣∣∣∣k=(∑

l /=k

∣∣hk,l∣∣2)−1

. (4)

2.2. Assumptions

The algorithm is derived under the following assumptions.

(i) We assume a perfect single-user frame synchronisationand timing recovery (i.e., for the kth signal on the kthbeam).

(ii) The matrix H is assumed time invariant on a burst du-ration, and unknown at the receiver.

(iii) Significant interferers are only located in adjacentcochannel cells: due to the regular reuse pattern, thereare at most 6 significant interferers on a beam [6].

Let us recall that the algorithm considered in the follow-ing is suboptimal (see Section 1 and [1]): it only performsinterference cancellation for the kth signal at the output ofthe kth beam.

3. ALGORITHM DESCRIPTION ON A TIMEINVARIANT CHANNEL

3.1. Synchronous case

To simplify the presentation, we first consider a symbol-synchronous time-invariant channel, that is, τk = 0 andϕk(t) = ϕk for all k. After optimal sampling, we can thenconsider the “one-shot” approach with

y[n] = Gd[n] + n[n], (5)

J. P. Millerioux et al. 3

yK [n] Initial phaserecovery

DecodingEstimation

of gK,.

Interferencecancellation

d(m)k [n]

To beam l, for kinterfering on beam l

yk[n] Initial phaserecovery

y(m)k [n]

DecodingEstimation

of gk,.

Interferencecancellation

y(m+1)k [n]

d(m)l [n]

From beam l, for linterfering on beam k

y1[n]Initial phase

recovery DecodingEstimation

of g1,.Interferencecancellation

Figure 2: Block diagram of the receiver (synchronous case).

where

G = [gT1 · · · gT

K

]T = (gk,l) = H diag

(ρk exp

(jϕk))

,

d[n] = [d1[n] · · ·dK [n]]T

,

y[n]=[y1[n] · · · yK [n]]T

with yk[n]= yk(t)∗ s(−t)|t=nT ,

n[n]=[n1[n] · · ·nK [n]]T

with nk[n]=nk(t)∗ s(−t)|t=nT ,

E(

n[k]n[l]) = δ(k − l)Rn.

(6)

A synoptic of the receiver is given in Figure 2, where inter-leaving and deinterleaving operations are omitted for sim-plicity. All operations are performed in parallel on the dif-ferent beams, with exchange of information from one to an-other. The main steps are described in the following. For anyparameter c, c(m) denotes an estimate or a decision on c at themth iteration.

Channel estimation

The channel estimation on the kth beam is processed bya least-square estimator using currently estimated symbols(and including pilot symbols). At the mth iteration, we getfor the kth beam

g(m)k =

(N−1∑

n=0

yk[n]d(m)[n]H)(N−1∑

n=0

d(m)[n]d(m)[n]H)−1

.

(7)

We only use for estimation (and consequently for interfer-ence cancellation in (8)) estimated symbols of the useful sig-nal and of adjacent interfering ones (see Section 2.2. assump-tion (iii)), which is not specified in the equations for the sakeof simplicity.

Interference cancellation

The interference cancellation block output at the mth itera-tion (or the decoding block input at the (m + 1)th iteration)is for the nth symbol of the kth user

y(m+1)k [n] = g(m)∗

k,k

(yk[n]−

∑

l /=kg(m)k,l d

(m)l [n]

). (8)

In the case of perfect channel estimation and interferingsymbol decisions, we get

y(m+1)k [n] = ∣∣gk,k

∣∣2dk[n] + g∗k,knk[n], (9)

interference is entirely removed, and the carrier phase is per-fectly compensated.

Decoding

Decoding is performed by the Viterbi algorithm, by assimi-lating the residual interference plus noise after deinterleavingat the decoder input to AWGN.

Initialization

For the kth user, an initial carrier phase is estimated frompilot symbols on the kth beam. After phase compensation,the signal received on the kth beam is sent to the decodingblock to initialize the iterative process.

3.2. Asynchronous case

We now consider a symbol-asynchronous time-invariantchannel, that is, τk /= τl for k /= l, and ϕk(t) = ϕk for all k.We introduce

uk(t) =N−1∑

n=0

dk[n]s(t − nT − τk

),

u(m)k (t) =

N−1∑

n=0

d(m)k [n]s

(t − nT − τk

),

(10)

and vectors u(t) = [u1(t) · · ·uK (t)]T and u(m)(t) =[u(m)

1 (t) · · · u(m)K (t)]T .

We get

y(t) = Gu(t) + n(t), (11)

where G is defined in Section 3.1. We refer to u(m)k (t) as the

estimated kth signal at the mth iteration.The algorithm on the asynchronous channel is then very

similar to the one on the synchronous channel. For the kthbeam, at the mth iteration:

(i) channel estimation is processed by a least square ap-proach using the estimated signals at the matched fil-ter output u(m)(t) ∗ s(−t) and yk(t) ∗ s(−t), syn-chronously sampled, with 2 samples per symbol (sam-

ples of u(m)(t)∗s(−t) corresponds to d(m)[n] and sam-ples of yk(t)∗ s(−t) corresponds to yk[n] in (7));


11 12 13 14

8 9 10

4 5 6 7

1 2 3

(a)

Cell numberNumber ofinterferers

C/I [dB]

1, 3 3 5

2 4 4

4, 7 3 5

5, 6 6 2

8, 10 5 3

9 6 2

11, 14 2 6

12, 13 4 4

(b)

Figure 3: Description of the studied configuration.

(ii) interference cancellation is processed at 1 sample persymbol, at optimal sampling instants.

More details on the implementation can be found in [1].

3.3. Simulation results

We use for the evaluation the fictitious configuration de-scribed in Figure 3 (which is interference configuration 2 in[1]). We consider 14 cochannel beams. The 14 users havean equal SNR. For each cell, assumption (iii) of Section 2.2is perfectly respected, and interference is equally distributedamong the interfering cells: for example we have for cell 1h1,1 = 1, h1,2 = h1,4 = h1,5 = (3 · C/I|1)−1/2, and other coef-ficients of the first row of H are set to zero. We consider thefollowing simulation parameters.

(i) Rate 1/2 nonrecursive nonsystematic convolutionalcode with constraint length 7 and generators (133,171) in octal.

(ii) Packets of 53 information bytes (ATM cell), or 430 in-formation symbols (with closed trellis).

(iii) 32 pilot symbols, leading finally to N = 462 transmit-ted symbols in a burst.

Users timings τk are independent and uniformly distributedon [0,T]. Carrier phases ϕk are independent and uniformlydistributed on [0, 2π]. Additive noises are uncorrelated. Newrandom interleavers and training sequences are generated ateach burst.

We consider a target bit error rate (BER) equal to 2·10−4,which is reached on AWGN channel with perfect synchroni-sation for Eb/N0 equal to 3.2 dB. Some results for cells 5 and6, which are symmetric, are given in Figure 4. The algorithmexhibits a degradation with respect to single-user referenceof 0.15 dB after 3 iterations. At first iterations, the modulusestimate of g5,9 and g6,9 (which are symmetric) is widely bi-ased: it is underestimated due to imperfect symbol decisions.As the algorithm converges, this bias is removed. In the sameway, the unbiased phase estimate of g5,9 and g6,9 shows anerror standard deviation decreasing with iterations, until it

reaches the Cramer-Rao bound (CRB). This bound is moreprecisely the phase single-user modified CRB [9], given withour notations by

CRB(Arg

(gk,l)) = 1

2N

∣∣hk,l∣∣2(EsN0

)−1[Rd2]. (12)

Notice that these simulation results and all the following onescorrespond to at least 20 packet errors and 200 binary errorsfor each user. Consider as an example the results at iteration 3for Eb/N0 = 2.5 dB, our evaluation of confidence intervals at95% leads to [4.8, 5.9]·10−3 for the BER of cell 5, [1.2, 12.1]·10−3 for the modulus bias of coefficient g5,1, and [4.61, 4.89]◦

for the phase error standard deviation of coefficient g5,1.

4. EXTENSION TO THE CASE OFFREQUENCY OFFSETS

In geostationary systems, frequency offsets between the emit-ter and the receiver are mainly due to frequency instabilitiesof local oscillators. Considering the use of the Ka-band withlow-cost user terminals, they are inevitable. In order to helpthe receiver to recover these frequency offsets, synchronisa-tion bursts, which are periodically transmitted, are definedin the DVB-RCS standard. However, it always remains resid-ual frequency offsets on the traffic bursts. In case of shortbursts and low SNR, frequency and phase recovery becomea challenging task, especially with a reduced number of pilotsymbols.

In the following, we study possibilities of adaptation ofthe interference cancellation algorithm to the case of fre-quency deviations affecting user terminals. We first evaluatethe algorithm sensitivity to frequency offsets in Section 4.1.We find that it is only suited to very low frequency offsets. Wethen evaluate in Section 4.2 the use of block processing forestimation of beamforming coefficients in order to cope withhigher frequency offsets. As this approach is shown to leadto possible significant degradations, we finally propose and


0 0.5 1 1.5 2 2.5 3 3.5 4

Eb/N0 (dB)

10−5

10−4

10−3

10−2

10−1

100

BE

R

BER (cells 5 and 6)

No MUDPIC 1PIC 2

PIC 3Reference

(a)

2 2.5 3 3.5 4

Eb/N0 (dB)

−0.1

0

0.1

0.2

0.3

0.4

Nor

mal

ized

bias

()

Modulus estimate of g5,9 and g6,9

PIC 1PIC 2PIC 3

(b)

2 2.5 3 3.5 4

Eb/N0 (dB)

4

6

8

10

12

Err

orst

and

ard

dev

iati

on(◦

)

Phase estimate of g5,9 and g6,9

PIC 1PIC 2

PIC 3CRB

(c)

Figure 4: Results with time-invariant phases.

evaluate in Section 4.3 different schemes based on a single-user frequency estimator.

Notice the following:

(i) we possibly consider the use of pilot symbols dis-tributed within the burst (which is not possible whilestrictly following the DVB-RCS standard);

(ii) all numerical values of frequency offsets are given fora burst of 462 symbols (430 information symbols and32 pilot symbols).

4.1. Algorithm sensitivity to reduced frequency offsets

We evaluate in this section the algorithm sensitivity to re-duced frequency offsets. As a worst case (which is the clas-sical approach for single-user phase recovery) is difficult to

define in a multiuser context, we choose here to evaluate amean case. We model carrier phases ϕk(t) as

ϕk(t) = ϕk + Δ fkt, (13)

for all k, where the ϕk are independent and uniformly dis-tributed on [0, 2π], and the Δ fkT follow independent zero-mean Gaussian distributions with standard deviation σΔ f T .No change is performed on the algorithm, which assumestime-invariant phases, but pilot symbols are set in the mid-dle of the bursts (to avoid too biased initial phase estimates).Other simulation parameters are those of Section 3.3.

Some results in term of degradation with respect tosingle-user reference to reach the target BER are shown inFigure 5. Notice that the BER is independent of the sym-bol locations in the burst due to the use of interleavers. Thealgorithm appears maintainable with σΔ f T = 10−4, but thedegradations with σΔ f T = 2 · 10−4 are very large.


0 1 1.5 1.75

Standard deviation of 104·Δ f ·T

0

0.5

1

1.5

Deg

rad

atio

n(d

B)

Single userPIC 2 cells 4 and 7PIC 3 cells 4 and 7

PIC 2 cells 5 and 6PIC 3 cells 5 and 6

Figure 5: Degradation with frequency offsets.

32 64 128 256 462

Length of windows for estimation (symbol)

0

0.5

1

1.5

Deg

rad

atio

n(d

B)



Figure 6: Degradation with reduced estimation windows.

By comparing the degradations in single-user and mul-tiuser cases, we can see that they are similar for σΔ f T = 10−4

and for σΔ f T = 0 (i.e., without frequency offsets). We canconclude that the degradation in the multiuser case withσΔ f T = 10−4 is mainly due to imperfect user phase recovery.Beyond σΔ f T = 10−4, it can be observed that the degradationin the multiuser case increases more quickly than the degra-dation in the single-user case: interference cancellation effi-ciency is limited. The considered algorithm is consequentlylimited to about σΔ f T = 10−4 for a burst length equal to 462symbols.

4.2. Approach with reduced estimation windows forchannel estimation

In order to cope with higher frequency offsets, we use in thissection a classical block processing: the channel is no moreconsidered invariant on the whole burst, but is consideredinvariant on windows of reduced length. The algorithm ismodified in this way: channel estimation (7), which includescarrier phase estimations, is performed on reduced windows.Interference cancellation and phase compensation (8) is thenperformed on each window using the corresponding esti-mated coefficients gk,l.

Channel estimation sensitivity to frequency offsets de-creases when the length of estimation windows decreases, be-cause the constellation rotations on a window are reduced.However, sensitivity to additive noise increases when thelength of estimation windows decreases, because noise is av-eraged on shorter windows. The optimal length of estimationwindows then results from a tradeoff between frequency off-sets and noise.

We evaluate in this section the effect of reduced estima-tion windows without frequency offsets. Pilot symbols forinitialization are uniformly distributed on the burst. Someresults in term of degradation are shown in Figure 6. Thedegradation increases when the length of windows decreases.This is partially due to the fact that CRB for estimation of gk,l

increase while the length of windows decreases, leading to aless-efficient interference cancellation and phase compensa-tion in (8). However, the degradation is much more impor-tant for cells 5 and 6 than for cells 4 and 7, whereas the CRBfor channel estimation are equal in both cases (as we have|g5,2| = |g5,6| = |g5,9| = |g5,8| = |g5,4| = |g5,1| = |g4,1| =|g4,5| = |g4,8|). In fact, it can be seen in Figure 7 that similarlyto single-user phase estimation, our channel estimator takesdown from the CRB with short estimation windows and lowSNR. It appears much more critical for cells 5 and 6 than forcells 4 and 7, as the least square estimation is performed on7 (6 + 1) coefficients in the first case, and only 4 (3 + 1) inthe second case. This effect also appears for longer channelestimation windows, but it is less obvious to see it.

Notice that in order to optimize the length of windowsfor a given σΔ f T , we would consequently have to consider dif-ferent lengths of windows for the different cells: the optimallength would be shorter for cells 4 and 7 than for cells 5 and6.

The main conclusion is that the use of reduced estima-tion windows to cope with higher frequency deviations canlead to a significant loss (let us recall that evaluations havebeen performed in this section without frequency offsets),particularly for cells with a high number of interferers.

4.3. Approach with single-user frequency estimations

As the previous approach does not appear sufficient to copewith higher frequency offsets without a significant degrada-tion, we study in this section another approach. It is based onthe use of single-user frequency estimations.


2 2.5 3 3.5 4 4.5 5

Eb/N0 (dB)

5

10

15

20

25

30

35

40

45

Ph

ase

erro

rst

anda

rdde

viat

ion

(◦)

Coefficients g4,5 and g7,6

PIC 2, 32 symbolsPIC 3, 32 symbolsBCR, 32 symbolsPIC 2, 64 symbolsPIC 3, 64 symbols

BCR, 64 symbolsPIC 2, 128 symbolsPIC 3, 128 symbolsBCR, 128 symbols

(a)

2 2.5 3 3.5 4 4.5 5

Eb/N0 (dB)

5

10

15

20

25

30

35

40

45

Ph

ase

erro

rst

anda

rdde

viat

ion

(◦)

Coefficients g5,6 and g6,5

PIC 2, 32 symbolsPIC 3, 32 symbolsBCR, 32 symbolsPIC 2, 64 symbolsPIC 3, 64 symbols

BCR, 64 symbolsPIC 2, 128 symbolsPIC 3, 128 symbolsBCR, 128 symbols

(b)

Figure 7: Channel estimation errors for different coefficients and lengths of window.

CaseInitial PAfrequencyestimations

DD frequencyreestimations

Reducedestimationwindows for gk

a y n n

b y y n

c up to IT n n y

c beyond IT — y n

(a)

Windows for channel estimation

Case a

Case b

Case c

Pilot symbolsInformation symbols

(b)

Figure 8: Approach with frequency estimations: (a) operations performed, (b) distributions of pilot symbols.

4.3.1. Principle

If a frequency estimate Δ fk for the kth signal is available, it

can be included in the estimated kth signal: u(m)k (t) ∗ s(−t)

consequently becomes (u(m)k (t)∗ s(−t)) exp( j2πΔ fkt) in (7).

Since the constellation rotations on the burst for yk(t)∗s(−t)and (u(m)

k (t)∗ s(−t)) exp( j2πΔ fkt) are potentially very close

(ideally identical if Δ fk = Δ fk), it is then possible to keeplarge estimation windows to perform estimation in (7): us-ing the whole burst allows obtaining the minimum degra-dation. Clearly, this approach requires “accurate” single-userfrequency estimations, which become the hard task.

A first possibility is to use initial frequency estimationsbefore interference cancellation. In this case, the estimation

accuracy is limited due to the very low signal-to-interference-plus-noise ratio (unless using a very high number of pilotsymbols, which decreases the spectral efficiency). Anotherway is to use symbol decisions for frequency estimation ifit is possible to obtain sufficiently reliable symbol decisions.Many different receiver architectures can be derived. Threeexamples of architectures are described and evaluated in thefollowing sections.

4.3.2. Architectures with single userfrequency estimations

Two modes are considered for single-user frequency esti-mation: the pilot aided mode (PA), based on pilot sym-bols, and the decision directed mode (DD), based on symbol


2 2.5 3 3.5 4

Eb/N0 (dB)

10−5

10−4

10−3

10−2

BE

R

BER (cells 5 and 6)

No MUDPIC 1PIC 2

PIC 3Reference

(a)

2 2.5 3 3.5 4

Eb/N0 (dB)

10−4

Err

orst

anda

rdde

viat

ion

()

Frequency estimate (cells 5 and 6)

No MUD

(b)

2 2.5 3 3.5 4

Eb/N0 (dB)

−0.1

0

0.1

0.2

0.3

0.4

Nor

mal

ized

bias

()

Modulus estimates of g5,9 and g6,9

PIC 1PIC 2PIC 3

(c)

2 2.5 3 3.5 4

Eb/N0 (dB)

4

6

8

10

12

Err

orst

anda

rdde

viat

ion

(◦)

Phase estimates of g5,9 and g6,9

PIC 1PIC 2

PIC 3CRB

(d)

Figure 9: Results with frequency estimations: σΔ f T = 2 · 10−4, case a.

decisions. For the PA mode, pilot symbols are distributedwithin the burst into 3 blocks (see Figure 8(b), cases a andb). We follow the approach of [10]. First, a mean phaseis computed on each block of pilot symbols. Then, a leastsquare estimation based on these mean phases is used toestimate the frequency. For the DD mode, the principleis the same: the burst is divided into adjacent blocks, onwhich mean phases are computed using symbol decisions.For the DD mode, frequency estimations are performed

after interference cancellation, that is, Δ f (m)k are used to

obtain g(m+1)k .

The CRB considered for frequency estimation in DDmode is the single-user frequency modified CRB [9], givenby

CRB(Δ fkT

) = 32π2N3

(EsN0

)−1

. (14)

For PA frequency estimation, the CRB is different from (14)with N replaced by the number of pilot symbols (becausepilot symbols are not consecutive).


2 2.5 3 3.5 4

Eb/N0 (dB)

10−5

10−4

10−3

10−2

BE

R

BER (cells 5 and 6)

No MUDPIC 1PIC 2

PIC 3Reference

(a)

2 2.5 3 3.5 4

Eb/N0 (dB)

10−4

Err

orst

anda

rdde

viat

ion

()


No MUDPIC 1

PIC 2CRB

(b)

2 2.5 3 3.5 4

Eb/N0 (dB)

−0.1

0

0.1

0.2

0.3

0.4

Nor

mal

ized

bias

()


PIC 1PIC 2PIC 3

(c)

2 2.5 3 3.5 4

Eb/N0 (dB)

4

6

8

10

12E

rror

stan

dard

devi

atio

n(◦

)Phase estimates of g5,9 and g6,9

PIC 1PIC 2

PIC 3CRB

(d)

Figure 10: Results with frequency estimations: σΔ f T = 2 · 10−4, case b.

The following three cases of receiver architecture are eval-uated.

Case a

PA initial frequency estimations are performed, no frequencyreestimation is performed, the estimation window for the gkis the whole burst.

Case b

PA initial frequency estimations are performed, frequenciesare reestimated in DD mode at each iteration, the estimationwindow for the gk is the whole burst.

Case c

No initial frequency estimation is performed:

(i) for iterations up to IT: no frequency estimation is per-formed, the estimation window for the gk is 154 sym-bols for all cells (see Figure 8(b));

(ii) for iterations beyond IT: frequencies are reestimatedin DD mode, the estimation window for the gk is thewhole burst.

The operations performed are summarized in Figure 8(a). Inall cases, we use 32 pilot symbols. Distributions of pilot sym-bols are shown in Figure 8(b).


2 2.5 3 3.5 4

Eb/N0 (dB)

10−5

10−4

10−3

10−2

BE

R

BER (cells 5 and 6)

No MUDPIC 1PIC 2

PIC 3PIC 4Reference

(a)

2 2.5 3 3.5 4

Eb/N0 (dB)

10−4

Err

orst

anda

rdde

viat

ion

()


PIC 1PIC 2CRB

(b)

2 2.5 3 3.5 4

Eb/N0 (dB)

−0.1

0

0.1

0.2

0.3

0.4

Nor

mal

ized

bias

()


PIC 3PIC 4

(c)

2 2.5 3 3.5 4

Eb/N0 (dB)

4

6

8

10

12

Err

orst

anda

rdde

viat

ion

(◦)


PIC 3PIC 4CRB

(d)

Figure 11: Results with frequency estimations: σΔ f T = 2 · 10−4, case c.

4.3.3. Results with σΔ f T = 2 · 10−4

We first consider in this section a target σΔ f T equal to 2·10−4.Some results are given in Figures 9, 10, and 11 (with

IT = 2) for cells 5 and 6.In case a (Figure 9), after initial frequency estima-

tion, the frequency error standard deviation is about 10−4.Iterative interference cancellation works, but leads to adegradation in term of BER, as in Section 4.1. The er-ror standard deviation on the phase of g5,9 and g6,9 is farfrom the CRB, clearly because of imperfect frequency esti-mates.

In case b (Figure 10), DD frequency reestimations allowto get a frequency error standard deviation close to the CRB.Hence, the phase estimate error standard deviation of g5,9

and g6,9 is much closer to the CRB than in case a. The BERdegradation is the same as that in the case without frequencyoffsets in Section 3.3.

In case c (Figure 11), interference cancellation is efficientbut converges slower than in cases a and b. Four iterationsare necessary in case c to get the BER reached with three iter-ations in case b.

With σΔ f T = 2 · 10−4, the most efficient architecture isconsequently architecture b. However, if architecture c leads


2 2.5 3 3.5 4

Eb/N0 (dB)

10−5

10−4

10−3

10−2

BE

R

BER (cells 5 and 6)

No MUDPIC 1PIC 2PIC 3

PIC 4PIC 5Reference

(a)

2 2.5 3 3.5 4

Eb/N0 (dB)

10−4

Err

orst

anda

rdde

viat

ion

()


PIC 3PIC 4CRB

(b)

2 2.5 3 3.5 4

Eb/N0 (dB)

−0.1

0

0.1

0.2

0.3

0.4

Nor

mal

ized

bias

()


PIC 4PIC 5

(c)

2 2.5 3 3.5 4

Eb/N0 (dB)

4

6

8

10

12

Err

orst

anda

rdde

viat

ion

(◦)


PIC 4PIC 5CRB

(d)

Figure 12: Results with frequency estimations: σΔ f T = 5 · 10−4, case c.

to a slower convergence of the algorithm, a significant advan-tage is that it appears more suited to high-frequency offsets,as we will see in the following section.

4.3.4. Results with σΔ f T = 5 · 10−4

We now consider a target σΔ f T equal to 5 · 10−4.For this range of frequency deviations, it is very difficult

to obtain reliable initial frequency estimates without a hugenumber of pilot symbols. On the contrary, architecture c

appears to work. After optimization, we use IT = 3 withwindow lengths for gk estimation from 60 to 100 symbols(depending on the number of interferers of the consideredcell, Section 4.2). Some results are given in Figure 12. ForEb/N0 equal to 3.2 dB, the block processing approach allowsobtaining a BER equal to about 8·10−3 at iteration 3, which issufficient to obtain reliable frequency estimates at the follow-ing iterations. The degradation in terms of BER at iteration 5is then similar to the case without frequency offsets.

Finally, notice that we have considered average BER alongthe paper. Actually, this average BER can hide some complete


1 106 212

Number of erroneous bits per packet

0

0.5

1

1.5

2

2.5×10−3

Pro

babi

lity

Distribution of erroneous bits

Cell 5 at 4σΔ f T , Eb/N0 = 3.5 dB

424 information bits

Figure 13: Distribution of erroneous bits: σΔ f T = 5 · 10−4, itera-tion 5.

failures in convergence of the algorithm on some bursts, lead-ing to a BER on these bursts much higher than the BER aver-aged on all bursts. These failures can result from realizationsof high-frequency offsets, from cycle slip occurrences orsimply from inaccurate frequency estimates. A simpleapproach to evaluate a probability of failure is to monitor thenumber of erroneous bits per burst at the algorithm output.We consider a worst case: all frequency offsets are random(Gaussian with a standard deviation σΔ f T) except frequencyoffset for cell 5, which is deterministic and equal to 4σΔ f T =2 · 10−3. The estimated distribution of the number of erro-neous bits per burst for cell 5 at iteration 5 for Eb/N0 equal to3.5 dB is shown in Figure 13. We define a failure occurrencewhen the fraction of erroneous bits in a burst exceeds onefourth of the total bits in the burst (106 = 53 · 8/4). We de-duce a probability of failure equal to 2·10−3. In the same way,with a frequency offset for cell 5 equal to 3σΔ f T = 1.5 · 10−3,we deduce a probability of failure equal to 10−4.

5. CONCLUSION

We have studied in this paper an iterative multiuser detectionscheme, which includes channel estimation, suited to the re-verse link of multibeam satellite communication systems. Wehave first derived the algorithm in the case of time invari-ant carrier phases. We have then discussed possible exten-sions to the case of frequency offsets affecting user terminals.Our main result is that if different approaches are possiblefor the first iterations, frequency offset estimations are nec-essary for final iterations in order to limit the degradation.Further works will consist in evaluations (and possibly al-gorithm modifications) with a more realistic channel modelincluding phase noise.

ACKNOWLEDGMENT

The authors would like to thank the reviewers for theirthoughtful and incisive comments about this paper.

REFERENCES

[1] J. P. Millerioux, M. L. Boucheret, C. Bazile, and A. Ducasse,“Iterative interference cancellation and channel estimation inmultibeam satellite systems,” International Journal of SatelliteCommunications and Networking, vol. 25, no. 3, pp. 263–283,2007.

[2] Digital Video Broadcasting (DVB), “Interaction channel forsatellite distribution systems,” December 2000, ETSI EN 301790.

[3] M. L. Moher, “Multiuser decoding for multibeam systems,”IEEE Transactions on Vehicular Technology, vol. 49, no. 4, pp.1226–1234, 2000.

[4] G. Caire, M. Debbah, L. Cottatellucci, et al., “Perspectivesof adopting interference mitigation techniques in the contextof broadband multimedia satellite systems,” in Proceedings ofthe 23rd AIAA International Communications Satellite SystemsConference (ICSSC ’05), pp. 25–28, Rome, Italy, September2005.

[5] M. Debbah, G. Gallinaro, R. Muller, R. Rinaldo, and A. Ver-nucci, “Interference mitigation for the reverse-link of inter-active satellite networks,” in Proceedings of the 9th Interna-tional Workshop on Signal Processing for Space Communications(SPSC ’06), Noordwijk, The Netherlands, September 2006.

[6] E. Lutz, M. Werner, and A. Jahn, Satellite Systems for Per-sonal and Broadband Communications, Springer, New York,NY, USA, 2000.

[7] J. P. Millerioux, “Techniques de detection multi-utilisateurspour les communications multifaisceaux par satellite,” Ph.D.dissertation, ENST, Paris, France, September 2006.

[8] L. C. Godara, “Application of antenna arrays to mobilecommunications—part II: beam-forming and direction-of-arrival considerations,” Proceedings of the IEEE, vol. 85, no. 8,pp. 1195–1245, 1997.

[9] A. N. D’Andrea, U. Mengali, and R. Reggiannini, “The mod-ified Cramer-Rao bound and its application to synchroniza-tion problems,” IEEE Transactions on Communications, vol. 42,no. 234, pp. 1391–1399, 1994.

[10] F. Adriaensen, W. Steinert, and A. Van Doninck, “MF-TDMAburst demodulator design with pilot symbol assisted fre-quency estimation,” in Proceedings of the 8th ESA Interna-tional Workshop on Signal Processing for Space Communications(SPSC ’03), Catania, Italy, September 2003.


Research ArticleA QoS Architecture for DVB-RCS Next GenerationSatellite Networks

Thierry Gayraud1, 2 and Pascal Berthou1, 2

1 Laboratoire d’Analyse et d’Architecture des Systemes (LAAS-CNRS), University of Toulouse, Cedex 4, 31077 Toulouse, France2 Toulouse University of Science, Toulouse, France

Received 1 October 2006; Revised 25 January 2007; Accepted 31 May 2007


The standardization of a return channel via satellite (DVB-RCS) and satellite community efforts in term of interoperability overthe last few years leads to quite a positive outcome: geostationary satellite networks are intended to provide broadband access tointeractive multimedia services in low-infrastructure areas. However, in order to take in account real-time multimedia traffic, anefficient resource management scheme is still necessary to maximize the scarce uplink capacities usage. To address this capacityissue, this paper proposes a complete DVB-RCS QoS architecture that is implemented, thanks to an emulation platform, andevaluated with real multimedia applications. This paper first gives an overview of the QoS architecture usually used in DVB-S/RCS satellite system, especially in layers 2 and 3. It then introduces the satellite system emulation used in the experimentationand its calibration. The main contribution of this work focuses on the signaling principle designed to allow applications to takebenefit from the QoS features of the satellite system even if they are non-QoS aware. It is then shown how signaling in such QoSarchitecture allows the user to change dynamically the QoS of his application using QoS agent and QoS server applications evenif the application is not QoS-aware. It is also given quantitative results related to such a dynamic QoS change in the experimentsdone on the satellite emulation system.

Copyright © 2007 T. Gayraud and P. Berthou. This is an open access article distributed under the Creative Commons AttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properlycited.

1. INTRODUCTION

Geostationary satellite access networks are expected to play,in a near future, a decisive role in next generation networks(NGNs) as they are intended to provide broadband accessto interactive multimedia services in low-infrastructure ar-eas. Known as a real complementary technology in geo-graphical locations beyond reach of terrestrial means, satel-lite networks still suffer, in comparison to terrestrial net-works, from long delays, scarce bandwidth resources, andequipment costs.

The standardization of the digital video broadcasting-return channel via satellite (DVB-RCS) in March 2000 andthe publication of the guideline document in September2001 stand for major milestones in the development of re-liable, efficient, and low-cost satellite equipment through theharmonization of RCS terminals (ST) based on this openstandard. Several commercial DVB-RCS based networks arealready deployed and many efforts are done in order to en-hance interoperability.

Most recent commercial deployments provide either In-ternet access or mesh connectivity over a transparent geo-stationary satellite. Fixed bandwidth contracts are generallyoffered to consumers, thanks to a simple resource manage-ment scheme. It simplifies admission control, reduces cost,and gains experience while waiting for the standardizationof finer resource management strategies and equipment. Alot of work on IP over satellite remains particularly in thequality-of-service (QoS) field and the next step is, obviously,to take benefits from DVB-RCS dynamic allocation schemesand IP QoS architectures to cope with the satellite delay andthe scarce uplink resources.

This article proposes QoS architecture compliant withthe recommendation made by the ETSI BSM (broadbandsatellite systems) working group which provides a state of theart of existing QoS mechanisms that are applicable to broad-band multimedia satellite systems [1].

The implementation made in a satellite emulation plat-form represents a first attempt to evaluate a complete DVB-RCS QoS architecture and a set of new services in a system


based on either a regenerative or transparent satellite that willbe the future of satellite networks.

This paper proceeds in the following way. Section 2 givesan overview of new trends in next generation satellite sys-tems and sums up the principle of the DVB-RCS standard.Section 3 describes the features of our QoS architecture. TheQoS signalling principle is explained here. Then, Section 4shows our satellite emulation platform and an evaluation ofthe new services provided by the QoS architecture, demon-strating especially the dynamic QoS change features.

2. NEW TRENDS IN SATELLITE SYSTEMS

2.1. Forward link

The first DVB norm described a transmission scheme basedon MPEG-2 (Motion Picture Expert Group) video compres-sion and transmission schemes, using MPEG-TS (MPEG-transport stream). This latter was adapted for satellite sys-tems through DVB-S (DVB transmission via satellite) thatdefines series of options to send MPEG-TS packets over satel-lite links and that is currently used for digital TV. The suc-cess of this standard has caused its adoption for Internet ser-vices over satellite. Then, the encapsulation of IP over MPE(multiprotocol encapsulation) or more recently ULE (ultralightweight protocol) is needed. This leads to a complex net-work stack. DVB-S2 standard [2] is intended to be a suc-cessor of DVB-S with the same applications (TV, Internet,etc.). It offers new coding techniques that can increase per-formance by 25% over that of DVB-S, but is still compati-ble with encapsulation layers as MPE or ULE. An alternativeknown as GS (generic stream) intends to gain direct access tothe physical layer, avoiding the MPEG2-TS packet overhead,but this protocol remains a work in progress.

The satellite terminals could therefore only receive DVB-S/S2 frames from the satellite, but did not have the ability tosend any traffic towards the satellite.

2.2. Return link

In 1999, the ETSI proposed a standard for a return channelvia satellite, the DVB-RCS [3, 4], which supplements the STswith the ability to transmit traffic towards the satellite.

According to this basis, two types of satellite can be de-fined.

(i) Transparent satellite simply forwards the signal re-ceived with no additional processing. A gateway (GW)is needed on the ground to convert DVB-RCS framesinto DVB-S one. Each communication goes throughthe gateway with a “star” topology. The delay to crossthe satellite network is about half a second and a dou-ble hop (at least 1 second) is needed to connect twosatellite users.

(ii) Regenerative satellite with onboard switching payloadis able to demodulate, process, and remodulate thetraffic that goes though it and therefore to multiplexseveral DVB-RCS signals into a single DVB-S one. Theassociated topology could be a “star” or a “meshed”

network. The end-to-end delay decreases to only onesingle hop.

Furthermore, DVB-RCS requires a medium access con-trol (MAC) protocol because satellite terminals (ST) are ableto simultaneously access the return channel capacity. Thestandard method relies on a multifrequency time divisionmultiple access (MF-TDMA). It basically relies on the avail-ability of several TDMA channels (corresponding to differentcarrier frequencies), each subdivided into frames and furtherinto timeslots of fixed length (bursts) during which the STsare able to transmit data through MPEG2-TS or ATM trafficbursts.

The entity responsible for this timeslot allocation withinthe superframe shared by competing STs is the NCC (networkcontrol center) that centralizes the satellite resources man-agement. Thus it periodically broadcasts a signaling frame,the TBTP (terminal burst time plan) that contains the infor-mation on which STs relies to know when to transmit theirbursts.

This allocation can be dynamically modified by STs re-quests so as to prevent from wasting satellite resources thatwould be otherwise statically allocated. The implementationof such a mechanism is generally known as bandwidth on-demand (BoD) algorithm.

2.2.1. Bandwidth on-demand mechanisms

In order to dynamically manage the bandwidth allocation,a bandwidth on demand protocol called demand assignmentmultiple access (DAMA) is defined. It relies on the STs abilityto request frequently “capacities” to the NCC which enables aregular update of the TBTP to fit to the STs respective trafficload. The latter provides signaling schemes as well as MACQoS classes and their mapping on capacity types.

Thus, the norm defines 4 capacity categories to fit the ap-plications needs:

(i) continuous rate assignment (CRA) which is static ca-pacity, not subject to dynamic requests;

(ii) rate-based dynamic capacity (RBDC), which is dy-namic rate capacity (in slots/frame), upper-boundedby MaxRBDC, granted in response to dynamic re-quests from the STs to track their instantaneous trafficrate;

(iii) (absolute) volume-based dynamic capacity (VBDC andAVDBC), which is also dynamic rate capacity (in slots),granted in response to dynamic requests from the STsto track their traffic queue state;

(iv) free capacity allocation (FCA), which is assigned to STson an “as available” basis from unused capacity.

Capacity types are vital to return path QoS support at MAClayer; therefore, they are described in detail in the following.Any given ST can be assigned one or a mix of the four capac-ity types. Generally, higher priority classes of service are asso-ciated with guaranteed capacity (CRA, RBDC), while lowerpriority classes are predominantly given best effort capacity(VBDC, FCA).

T. Gayraud and P. Berthou 3

Even if the service classes are properly defined, the allo-cation algorithms implemented in the NCC to fulfill the ser-vices requirements are not specified.

3. QoS ARCHITECTURE

This section describes the QoS architecture we propose forDVB-S/RCS satellite systems. The main contribution is builton return link management. Thus the downlink is generallyconsidered not to be a bottleneck and classical traffic engi-neering techniques are enough to managed the network.

3.1. Basis of QoS in satellite systems

To reach an optimal exploitation of uplink resources, at leastthree functions must be implemented to provide QoS guar-antees.

(i) QoS admission control consists, before the applicationsends its traffic, to check that the network has enoughresources. This prevents some applications from send-ing traffic that would otherwise lead to congestionamong high priority traffic.

(ii) QoS enforcement consists in checking that the admit-ted traffic respects its contracts, that is, that it doesnot use more resources than requested. This is doneby policing and shaping.

(iii) QoS differentiation consists in having several classes oftraffic, each class provides different behavior adaptedto a given service. This task is complex and needs dy-namic management during the connections lifetimeand must be performed at two layers: the DVB-RCSand IP layers.

Thanks to the 5 bandwidth allocation mechanisms in-cluded in DVB-RCS standard, the traffic differentiation ismade easily in introducing several MAC queues in the STstack and mapping the capacity requests over the MACqueues. Then, IP DiffServ-based router architecture can besetup over these new MAC services. However, this cannot bedone without cross-layer mechanisms that ensure perfect re-sources use.

3.2. Cross-layer architecture

The QoS management, in the proposed architecture, is splitinto three levels detailed in the following paragraphs.

(i) Satellite terminal resources: is medium access controllevel, where the DVB-RCS DAMA allocates the band-width on a fixed basis for real time applications and ondemand for other flows (nonreal-time traffic).

(ii) Class of service resources: a specific IP level module im-plements a queue management system aiming at pro-viding a differentiated service with regards to three ser-vice classes. These service classes are deemed to exploitthe capabilities offered by the MAC level QoS capabil-ities.

(iii) User level resources: this level is related to the share ofprevious services resource between the different users.

QoS AgentApplication

QoS signalling

QoS Server

MF-classifier IP classes

IP downstreamfrom user terminal

Traffic shaping/policing

Sch

edu

ling

EF AF BE

EDF EDF

PQ

/

EF AF + BE

Segmentation

IPL

ayer

Transmissionallowed/denied

IP DVB/RCSinterface

MA

Cla

yer

Threshold

RT DVBframes

NRT DVBframes

Framing

DVB-RCS frames

To satellite

DAMA client

DAMA server

TBTPCapacityrequests

To/from NCC

Figure 1: QoS architecture.

The user is able to classify its own flows in any availableservice through a dedicated agent (the QoS agent) thatcommunicates with the QoS server to deliver the clas-sification. The goal is to exploit the capabilities offeredby the IP QoS capabilities.

An overview of this QoS architecture within the ST is givenin Figure 1.

3.3. QoS at DVB-RCS layer

QoS management at the MAC layer aims at sharing with op-timal way the global uplink resources among the STs. Thus,the MAC layer must be able to

(i) provide strict guarantees in terms of delay and jitter;(ii) preserve these resources through fitting their alloca-

tion to the effective ST traffic load.

Within the ST MAC layer, the traffic is split into 2 classesof service (CoS), DVB-RT for “real-time service” and DVB-NRT for “nonreal-time” service, which are associated to2 different ATM permanent virtual channels (PVC). One(DVB-RT) benefits from static resource assignment through


CRA; on the contrary, (DVB-NRT) relies on a dynamic re-source allocation scheme also called BoD algorithm whichwill be further detailed in this section.

(i) Real-time queue: the CRA consists in a fixed capacitythat is set at the ST log-on and is not subject to renego-tiation during the ST connection lifetime. Each super-frame contains one or more slots assigned to this con-nection. This reserved static rate is entirely dedicatedto the DVB-RT traffic, since its high delay sensitive re-quirements hardly tolerates throughput fluctuations.

(ii) Nonreal-time queue: the request category retained forDVB-NRT traffic class is VBDC and FCA. Delay andjitter tolerant traffic is supplied by the MAC schedulerto the DAMA controller that computes the adequatedynamic volume to request to the NCC. These requestsare sent out of band, not in traffic slots assignments,but signaled in each SYNC slots broadcasted periodi-cally by the NCC.

This architecture uses an original DAMA protocol that aimsto reduce the allocation delays without reducing the networkuse.

As soon as an application produces a data, a free slot inthe next super frame should be available to send it. However,the allocation done with the DAMA protocol takes at least600 milliseconds (minimum scheduling latency—MSL). Toreduce its impact on the end-to-end delay, application needsare anticipated in monitoring the DVB-NRT queue lengththat grows conjointly. If the queue grows, the requested ca-pacity is increased by a factor α otherwise only the minimumis requested as. This algorithm is detailed in [5]. As shownlater, by properly setting α, the latency introduced by the BoDalgorithm can be effectively reduced.

In addition to the VDBC requests, the MAC scheduler inthe NCC distributes extra capacities to the logged STs if thenetwork is not congested. This last capacity category (FCA)comes out to enhance the ST performance especially on lowloading conditions, preventing the ST from waiting at leastfor the MSL to be able to transmit.

3.4. QoS at IP layer

In order to achieve a complete traffic control framework, aclassifier separates IP traffic into 3 categories:

(i) real-time: such an IP flow should be guaranteed a min-imum bandwidth, an upper bound on queuing delay,a mean queuing delay of a few tens of milliseconds;

(ii) nonreal-time: such an IP flow should be guaranteed aminimum bandwidth, a mean queuing delay of a fewhundreds of milliseconds;

(iii) best-effort: all IP packets not recognized as belongingto a particular IP flow are treated without any guaran-tee on bandwidth or delay.

The classifier then maps the packets to the 2 MAC categories.The overall goal of the architecture is to enforce the con-straints for the IP categories as defined above while maxi-mizing utilization of the available time-varying capacity.

With reference to IntServ/DiffServ traffic classes, thebest-effort (BE) traffic category supports the traditional ser-vice offered by the Internet by default without any specificQoS measure and whose performance are strongly impactedby network congestion states. Real-time IP data category in-cludes both IntServ guaranteed service class and DiffServ ex-pedited forwarding (EF) PHB (per-hop behavior) while thenonreal-time IP category is used for IntServ controlled loadservice class and DiffServ assured forwarding (AF) PHB [6].

3.4.1. QoS enforcement

The fundamental component of the architecture is theEDF scheduler preceded by token buckets (RC-EDF, rate-controlled earliest deadline first) which allows fixing and up-per bound to queuing delay and a minimum bandwidth forseparate IP flows. Namely, the presence of token buckets isa guarantee that each IP flow will receive a minimum band-width, given sufficient demand, equal to the relevant tokenrate, while the EDF scheduler will guarantee to each packetof an IP flow, once suitably regulated by a token bucket to beserved within a deadline equal to its associated static param-eter.

In Figure 1, the RC-EDF components are gathered underthe appellation “traffic shaping/policing.” The traffic polic-ing and shaping are then realized, thanks to single-rate tokenbuckets.

3.4.2. Layer 3/layer 2 mapping

The 3 traffic categories are served by a scheduler using a sim-ple priority queuing (PQ) discipline. This means that

(i) packets from NRT queues are served only when RTqueues get completely emptied,

(ii) packets in the BE queue are extracted only when RTand NRT queues are empty.

3.4.3. Application mapping

The EF traffic includes a number of real-time applicationswith stringent time and bandwidth requirements such astelephony or video conferencing. IP signaling which has verystringent delay requirements but which is characterized bylow-data rates should use this service class too.

The AF traffic should include a number of traditionalInternet applications to be served with a satisfactory levelof service and transported over TCP. They include telnet,HTTP, SMTP, FTP. Such applications can greatly vary interms of bandwidth and delay requirements. This means thatapplications such as telnet or HTTP should be assured smallqueuing delay though with limited bandwidth.

The BE class is designed to manage all traffic which isnot recognized as belonging to a particular user entitled toreceive better QoS or to applications with no particular delayor bandwidth requirement. SMTP or FTP should belong tothis class.


QoSsegregation

Satellite

ST

MAC

HubNCC

Router

IP

IPv4 , IPv6ST: satellite terminalMAC: medium access controlNCC: network control center

Figure 2: QoS signaling principle.

3.5. QoS signaling

The link between the applications and the QoS architectureis the QoS signaling. It allows the expression of the quality ofservice requested by an application and the configuration ofthe corresponding QoS provider.

In the proposed architecture (Figure 2), the QoS provideris the ST. An application who want to take advantage of agiven IP QoS service (EF, AF, BE) must configure the satel-lite terminal in order to redirect its packet on the appropriatequeue. A classical approach consists in statically configuringthe ST to associate a port to a service (e.g., the FTP port tothe best effort service). Usually done by the network admin-istrator, this approach does not work with a set of new appli-cations that open unfixed port as, for instance, VoIP applica-tions.

A more generic and “user-oriented” approach has beenproposed. The ST could be customized on the user request.Dedicated software, the QoS agent [7], allows to associatea running application to one of the three defined servicesand to send this association to the ST. It dynamically mon-itors application connections and sends to the ST the 5 tu-ples 〈source IP address, destination IP address, source port,destination port, type of protocol〉 for each of them. TheST maintains an association’s table. Each incoming packet isredirected within the ST to the appropriate queue accordingto this association’s table.

Figure 3 shows the six connections opened by Gnomeet-ing, videoconference software, and their selected services.

The QoS agent can be run as a daemon to apply predeter-mined rules without user interaction. In that case, it extendsthe “classical” approach with new applications.

4. EXPERIMENTAL MEASUREMENTS

4.1. Emulation principle

Evaluating performances over real data links or networksis expensive, even impossible for systems in developmentphase.

Figure 3: QoS agent user interface (GUI).

Simulation and emulation both provide the opportunityto evaluate performances, at low-cost, on more or less realis-tic systems. When simulation needs a complete modeling ofthe systems from applications to physical network and oper-ates in virtual time, emulation is more demonstrative sincereal applications can be deployed over the model describ-ing transfer characteristics, delay, and error behaviors for in-stance.

For these reasons, the choice was made to set up a satelliteemulation platform to demonstrate the network and applica-tion services integration on next generation satellite systemsand the possibility to interoperate with terrestrial networks.

4.2. Test bed

The network elements that belong to a classical satellite net-work (Satellite, NCC, STs) are emulated individually on adedicated computer. A gigabit Ethernet interconnects themand emulates the satellite carrier emulation. Ethernet waschosen for its native broadcast abilities and also for its highbandwidth capacities. Each satellite channel is mapped on asingle Ethernet multicast address.


4.2.1. Satellite link emulation

The satellite link emulator (SLE) simulates satellite link char-acteristics in term of delay (and distribution); bit-error rate(error burst frequency distribution, error burst length dis-tribution), computed according to precalculated distributionand based on real measurements.

Each channel crosses the link emulator to simulate theeffects of the two-way satellite link in real-time. The packetssent from an ST to the SLE are delayed and are also subject toa sequence of bit errors at random positions before they areforwarded to the emulated “downlink” (a multicast addressper spot).

4.2.2. Network control center

The NCC is the core of the satellite network management. Itdeals with allocating radio resources to the STs according totheir subscriber profile and available satellite resource. It cer-tainly implements a DAMA controller, but provides also anaddress resolution protocol to map IP addresses over under-lying protocols and a QoS admission mechanism.

4.2.3. Satellite terminals

The satellite terminals are based on Linux systems. They actas an access router interconnecting a LAN to an Internet ser-vice provider over a satellite link. Its DVB-S/DVB-RCS in-terfaces allow the data emission and reception and it imple-ments the corresponding network layers. The proposed QoSarchitecture is mainly located in the terminals.

The accuracy of the ST implementation is close to a pro-totype version and makes the emulation very realistic butalso critical for its configuration. The calibration of the ser-vices given to the users has been a touchy part of this work.

4.3. Platform calibration

As we explained in the former section, the available platformwill provide us with a prototype as close as possible to a realDVB-S/RCS system behavior. So the quantitative results per-formed on it are rather significant. To reach this result, theplatform has to be calibrated, that means that the right pa-rameters have to be set to the right value. If this stage is notproperly achieved, then the results offer no interest, even ifall the parts of the emulation testbed are very accurate. So, inthis section, the basic platform configuration chosen in orderto carry out our experimental measurements is detailed.

This configuration stands for the reference scenario fromwhich all the calibration adjustments are done in order toensure the significance of platform performance. Throughthis nonexhaustive list of the main platform configurationparameters, we emphasize the huge possibility to customizethe platform which still remains, even for simplified currentcommercial DVB-RCS deployments, a vital and difficult task.

4.3.1. Physical layer

The satellite diffusion properties are configured through theSE (delay, Jitter and Losses patterns) and the return link ca-

Table 1: Basic physical and MAC layer configuration.

Physicallayer

ST information peak rate 2048 Kbps

Superframe 10 Trames

Frame duration 50 ms

Global DVB-RCS resource 2048 Kbps

BasicDAMA

FCA None

α 1

SLA STCRA 96 Kbps

VBDC [FCA;1760 Kbps]

pacity segmentation scheme. The satellite emulator delay isset to 250 milliseconds, the jitter is equal to ±1 milliseconds,and the loss pattern is typical of a nice weather. Please notethat last notion which could sound subjective corresponds,in the satellite emulator, to real satellite measurement traces.

4.3.2. MAC layer

The main parameters are closely linked to resource sharingassignment from the NCC that distinguished two CoS at theMAC layer in the ST. The ST maximum transmission rate isshared by CRA and VBDC. Therefore, the peak transmissionrate is defined at first, then the CRA amount and finally theDAMA configuration through the α anticipation parameterand the FCA threshold (Table 1). The MAC queue sizes haveto respect minimum thresholds so as to prevent congestionfrom occurring in the MAC Layer.

4.3.3. IP layer

Considering that EF and AF services are implemented strictlyaccording to the single-rate token buckets and that there is noBE service conditioning, the main parameters of traffic con-ditioning blocks (TCB) and IP scheduling are summarized inTable 2.

4.4. Measurements

The measurements given in this section aims at evaluatingthe dynamic QoS change mechanism. First, the experimenta-tion done on DAMA results that have already been presentedin [5] are used to prove the right calibration of the emula-tion testbed, so that the result obtained further is realistic.The second part of the measurements has been performed ona multiflow scenario involving several applications. The ob-tained figures and tables show that the QoS architecture im-plementing the QoS server allows the user to change dynam-ically the QoS of one application thanks to the QoS agent.

4.4.1. Impact of FCA and α

The following study is linked to a VBR traffic source: a DIVXstreaming session. The DAMA influence cannot be neglectedin these experiments when the throughput variations can beabsorbed by the DAMA algorithm. Thus the basic DAMAperformances can be enhanced by increasing the anticipation


Table 2: IP TCBs and Scheduler configuration.

Service EF or “voice” AF or “FTP” BE

Token bucket size 172 bytes (GSM packet size) 1500 bytes (Ethernet MTU)No conditionning

Token rate 77.9 Kbps (∼= 96 Kbps CRA) 77.9 Kbps

FIFO size — — 500 000 bytes

EDF delay 20 ms 50 ms —

Max latency 25 ms 500 ms 5 s

21.510.50

Delay (s)

0

10

20

30

40

50

60

70

80

90

100

CD

F(%

)

α = 0α = 0.5α = 1

Figure 4: DAMA impact (VBR flow without FCA).

factor α which enables to bring 50% of the packets delay un-der 1 seconds (Figures 4 and 5).

Under 0.5, the anticipation factor does not improve theend-to-end delay. If we consider this factor, the reduction ofα leads to a capacity underutilization, it will be maintainedto 0.5 which stands for an interesting compromise betweenqueuing delays and uplink utilization efficiency (Figure 6).If FCA allocation is taken into account, an additional im-provement can be noticed. The factor α seems to have lessimpact on the end-to-end delay than in the first scenario.However, this 40 Kbps allocation stands for more than 10%of the DIVX average throughput and might be consideredas overestimated for a single ST. Therefore, the anticipationfactor has still a relative importance on VBR traffic which isdirectly linked to its average throughput and variability.

4.4.2. Global architecture under different loadingconditions

The purposes of different tests are to measure the SATIP6QoS performances under heterogeneous traffic flows (GSMVoIP sessions, DIVX VoD, FTP, and web browsing) whichare mapped onto the three different SATIP6 services. As seenpreviously, the voice service offers strict guarantees in termsof delay and jitter. The AF service (FTP) ensures a minimum

1.81.61.41.210.80.60.40.20

Delay (s)

0

10

20

30

40

50

60

70

80

90

100

CD

F(%

)

α = 0α = 0.5α = 1

Figure 5: DAMA impact on a VBR flow with FCA.

10097.59592.59087.58582.58077.575

Uplink utilization efficiency (%)

300

400

500

600

700

800

Qu

euin

gde

lay

(ms)

α = 1

α = 2/3

α = 1/2

α = 1/3

α = 0

Figure 6: Delay versus efficiency.

throughput and protects the AF traffic from losses in con-gestion state. Finally, the BE service is the most affected bycongestion while the satellite overload implies less capacitiesfor overall BE traffic and therefore higher delays and losses.

In Table 3, we can notice that voice service is not affectedby the loading conditions when the delay experimented byFTP and BE traffic increases. Inside the DVB-NRT trafficclass, FTP traffic is protected from losses at the expense ofthe BE class delay and loss ratio in congestion states.


120000100000800006000040000200000

Time (ms)

400

600

800

1000

1200

1400

1600

1800

2000

Th

rou

ghpu

t(k

bits

/s)

1 2 3 4

Throughput (kbits/s)

Figure 7: Dynamic change of class of service using the QoS agent.

Table 3: SATIP6 QoS performance under different loading condi-tions.

Networkload [%]

Average delay (Jitter) [ms] Losses [%]

BE FTP Voice BE FTP Voice

25 293 (26) 293 (26) 283 (23) 0 0 0

50 291 (23) 291 (24) 283 (23) 0 0 0

75 290 (24) 289 (24) 283 (23) 0 0 0

100 919 (23) 948 (24) 283 (23) 0 0 0

125 6753 (23) 1783 (24) 283 (23) 33 0 0

150 6755 (28) 1783 (24) 283 (23) 37 0 0

4.4.3. Dynamic change of QoS

The change of multimedia stream QoS is done thanks to QoSagent.

The different following steps are easy to find in Figure 7.

(i) Step 1: the scenario begins as a UDP video streamstarts. This stream is sent in the BE class of service.

(ii) Step 2: 25 seconds later, another flow is sent on thesame uplink; it is done so that the uplink is now con-gested. The throughput of the first stream is then re-duced to 800 kbps.

(iii) Step 3: 25 seconds later, the user decides to upgrade theclass of service of this stream and set it up to “voice.”After traffic burst, due to the addition of the EF serviceof 1 Mbps, and the traffic buffered before the resourcereservation, the throughput is around 1 Mbps.

(iv) Step 4: at t = 80 s, the stream is downgraded back to BEand the stream throughput is then around 800 kbps.

In Figure 7, the time needed to change from one Cos to an-other one for a flow could also be evaluated when the link iscongested by other data flows.

The delays given in Table 4 show as usually that the delayis around 3 seconds. It is less when a new flow is added on alink. It is longer when the QoS of a flow is upgraded and less

Table 4: Dynamic QoS change delay.

Transition 1 → 2 2 → 3 3 → 4

Initialsituation

One flowwithout QoS

Two flowswithout QoS

Two flows,one with QoS

Finalsituation


Two flows,one with QoS


Delay (s) 2.8 3.5 3.15

when it is downgraded, still longer in these two cases than inthe simple addition of a flow.

These results conclude the section dedicated to experi-mental measurements by putting the stress on the propertraffic differentiation carried out by our QoS architecture andthe ability to change from one class of service to the other onethanks to the QoS agent GUI.

5. CONCLUSION

It was proved in this paper that it was possible to specify andimplement QoS architecture for DVB-S/RCS satellite systemin order to provide the user with QoS guarantees even if anon-QoS-aware application is used. MAC algorithms (suchas DAMA) were proved to be efficient. It was also explainedhow to proceed to evaluate such an architecture. Using mea-surement tools on a well-calibrated testbed, the global QoSof the satellite system may be evaluated accurately.

Using other capacity category than VBDC (RBDC for in-stance) is improving resource utilization especially if appli-cations throughputs are known. Unfortunately, this is notusual today in the Internet. In that case, we propose to userate-based signaling protocols (SIP) in order to set up theright capacity requests.

Other future work may also be done related to DVB-S2and new admission control mechanisms.

ACKNOWLEDGMENTS

The authors wish to thank all the partners of the SATIP6[8] consortium: Alcatel Space (France), which is the projectcoordinator, Telecom Italia Lab (Italy), France Telecom SA(France), University of Rome “La Sapienza” (Italy), Sintef(Norway), LAAS-CNRS (France), and Alliance Qualite Logi-ciel (France).

REFERENCES

[1] ETSI TR 102 157, “Satellite Earth Stations and Systems (SES);Broadband Satellite Multimedia; IP Internetworking over satel-lite; Performance, Availability and Quality of Service,” July2003.

[2] ETSI Standard TR 102 376 V1.1.1, “Digital Video Broadcasting(DVB); User guidelines for the second generation system forBroadcasting, Interactive Services, News Gathering and otherbroadband satellite applications (DVB-S2)”.

[3] ETSI EN 301 790 V1.3.1, “Digital Video Broadcasting (DVB);Interaction channel for Satellite Distribution Systems,” March2003.


[4] ETSI TR 101 790 V1.2.1, “Digital Video Broadcasting (DVB);Interaction channel for Satellite Distribution Systems, Guide-lines for the use of EN 301 790,” January 2003.

[5] A. Pietrabissa, T. Inzerilli, O. Alphand, et al., “Validation ofa QoS architecture for DVB-RCS satellite networks via theSATIP6 demonstration platform,” Computer Networks, vol. 49,no. 6, pp. 797–815, 2005.

[6] J. Heinanen, F. Baker, W. Weiss, and J. Wroclawski, “RFC2597,Assured Forwarding PHB,” June 1999.

[7] S. Combes, O. Alphand, P. Berthou, and T. Gayraud, “Satelliteand next generation networks: QoS issues,” International Jour-nal of Space Communications, 2006.

[8] IST SATIP6 Project (Contract IST-2001-34344).


Research ArticleMaximum Likelihood Timing and Carrier Synchronization inBurst-Mode Satellite Transmissions

Michele Morelli and Antonio A. D’Amico

Department of Information Engineering, Via Caruso, 56100 Pisa, Italy

Received 4 August 2006; Revised 2 March 2007; Accepted 13 May 2007


This paper investigates the joint maximum likelihood (ML) estimation of the carrier frequency offset, timing error, and carrierphase in burst-mode satellite transmissions over an AWGN channel. The synchronization process is assisted by a training sequenceappended in front of each burst and composed of alternating binary symbols. The use of this particular pilot pattern results intoan estimation algorithm of affordable complexity that operates in a decoupled fashion. In particular, the frequency offset is mea-sured first and independently of the other parameters. Timing and phase estimates are subsequently computed through simpleclosed-form expressions. The performance of the proposed scheme is investigated by computer simulation and compared withCramer-Rao bounds. It turns out that the estimation accuracy is very close to the theoretical limits up to relatively low signal-to-noise ratios. This makes the algorithm well suited for turbo-coded transmissions operating near the Shannon limit.

Copyright © 2007 M. Morelli and A. A. D’Amico. This is an open access article distributed under the Creative CommonsAttribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work isproperly cited.

1. INTRODUCTION

Burst transmission of digital data and voice is widely adoptedin satellite time-division multiple-access (TDMA) networks.In these applications the propagation medium can be reason-ably modeled as an additive white Gaussian noise (AWGN)channel and knowledge of carrier frequency, symbol timing,and carrier phase is necessary for coherent demodulationof the received waveform. In the presence of nonnegligiblephase noise and/or oscillator instabilities, differential detec-tion is often employed to overcome the inherent difficultyposed by the phase estimation process. Even with differen-tial detection, however, the problem of timing and frequencyoffset recovery still remains.

Depending on their topology, synchronization circuitscan be divided into two main categories: feedback and feed-forward schemes [1, 2]. The former have good tracking ca-pabilities but exhibit comparatively long acquisitions due tohang-up phenomena [3–5]. The latter have shorter acqui-sitions and, accordingly, are better suited for burst-modetransmissions. In many cases, a preamble of known sym-bols is appended at the beginning of each burst to assist thesynchronization process. Actually, the use of a preamble al-lows data-aided (DA) operation and provides better estima-

tion accuracy as compared to a non-data-aided (NDA) ap-proach. Even so, however, synchronization may prove diffi-cult, especially with turbo-coded modulations operating atrelatively low signal-to-noise ratios (SNRs). Clearly, very ef-ficient synchronization algorithms are needed in these con-ditions [6].

The common approach to solve the synchronizationproblem in burst-mode transmissions is to estimate the tim-ing error first, and then use the time-synchronized samplesfor frequency and phase recovery. Two prominent feedfor-ward schemes for NDA timing estimation are investigatedin [7, 8]. In particular, timing estimates are derived in [7]by searching for the maximum of an approximate versionof the likelihood function while in [8] the received signal issampled at some multiple of the symbol rate and a square-law nonlinearity (SLN) is employed to wipe the modula-tion out. As shown in [2], the method in [8] is an efficientway of maximizing the likelihood function of [7] as longas the bandwidth of the complex envelope of the transmit-ted signal does not exceed the signaling rate. Since the useof a SLN exhibits poor performance in the presence of nar-rowband signaling, alternative methods employing absolutevalue or fourth order-based nonlinearities have been devised[9]. The main advantage of the timing estimators in [7–9] is


that they can operate correctly even in the presence of carrierfrequency offsets (CFOs) as large as 20% of the symbol rate.

Frequency estimation is usually performed by exploitingthe received time-synchronized samples. A large number ofschemes proposed in the past operate in either the frequencyor time domain. The Rife and Boorstyn (R&B) algorithm[10] belongs to the former class and provides maximum like-lihood (ML) estimates of frequency and phase errors by look-ing for the peak of a periodogram. Interpolation techniquesmay be employed to find an explicit expression of the peaklocation [11]. In the time-domain approach, suitable corre-lations of the received samples are exploited to compute thefrequency estimates. A representative selection of schemesderived along this line of reasoning can be found in [12–15].These methods attain the Cramer-Rao lower bound (CRB) atintermediate/high SNRs, but exhibit different performancein terms of estimation range and threshold, that is, the SNRbelow which large estimation errors are likely to occur.

A possible drawback of conventional frequency estima-tion schemes as those discussed in [10, 12–15] is that they allassume ideal timing synchronization. Their performance isthus limited by the accuracy of the timing estimator. A DAalgorithm for the joint estimation of the carrier phase, fre-quency offset, and timing error has been proposed in [16] byresorting to ML arguments. In order to work properly, how-ever, the demodulated signal must incur negligible phase ro-tations during the preamble duration. This poses a stringentlimit to the maximum tolerable CFO, which may prevent theapplication of this method to many practical situations.

In the present paper we are concerned with the joint esti-mation of all synchronization parameters for a burst-modesatellite system operating over AWGN channels. Since onedistinct feature of packetized transmissions is that synchro-nization must be achieved as fast as possible, in the follow-ing we only focus our attention to a feedforward structure.Also, we assume that a preamble of alternating binary sym-bols is transmitted at the beginning of each burst to facili-tate the timing estimation task [17]. Our approach is basedon ML methods and leads to a three-step procedure. Inthe first step frequency recovery is accomplished through amono-dimensional grid search. The estimated CFO is thenexploited in the second step to obtain a closed-form expres-sion of the timing estimate. The final step is devoted to phaseestimation and can be skipped in case of differential datadetection. Surprisingly, no complicated multidimensionalsearches are needed to jointly estimate all the unknown syn-chronization parameters. Simulations indicate that the pro-posed estimator is well suited for turbo-coded transmissionssince its accuracy approaches the relevant CRBs even at lowSNR values. However, it should be observed that this advan-tage is achieved at the price of a higher computational com-plexity as compared to other existing alternatives.

The paper is organized as follows. In Section 2 we in-troduce the signal model and formulate the synchronizationproblem. Section 3 illustrates the joint ML estimation of theunknown parameters and discusses in some detail the prac-tical implementation of the frequency estimator. In Section 4we derive CRBs to characterize the ultimate accuracy of fre-

quency, timing, and phase estimates. Simulation results arepresented in Section 5 while some conclusions are drawn inSection 6.

2. SYSTEM MODEL AND PROBLEM FORMULATION

2.1. Statement of the problem

We consider the reverse link of a satellite communicationsystem and assume a time-division multiple-access (TDMA)scheme where each earth station transmits bursts of data. Thestructure of a burst is detailed in Figure 1. Essentially, it con-sists of two parts: a header section followed by a payload. Theheader is further divided in two portions, namely, a synchro-nization preamble and a unique word (UW). The preamble ismade of a sequence of training symbols which are exploitedby the receiver for carrier and symbol timing recovery. TheUW is located just after the preamble and is used for burstidentification as well as to establish the start of the payload.

The first task of the receiver is the start of burst (SoB) de-tection, that is, the recognition of the time-of-arrival (ToA)of a generic burst. This is normally performed through a sim-ple noncoherent energy-detection scheme which provides acoarse estimate of the position of each burst. Once the SoBhas been identified, the preamble is exploited for carrier andsymbol timing synchronization. This is the second task of thereceiver and represents the focus of our paper. In order to ex-plain how synchronization can be achieved, we concentrateon a single burst and assume that the SoB detection algo-rithm has provided a ToA estimate with an error τ, as shownin Figure 2. The offset τ can be decomposed as follows:

τ = ηT − εT , (1)

where T is the symbol period, η is an integer (integer delay),and ε ∈ [−0.5, 0.5) is a real-valued parameter (fractional de-lay). During the preamble we are interested in the estimationof the fractional delay, because the integer delay is recoveredlater by searching for the location of the UW within the burst.The estimation of the synchronization parameters (fractionaldelay, carrier phase, and frequency offsets) is performed byobserving a portion of the preamble of length NT (N is a de-sign parameter) at the right of the assumed SoB, as shown inFigure 2. Clearly, the total duration of the preamble has to belarger than τ +NT . Since τ is a random variable, this condi-tion can be practically met by a proper design of the preamblelength. Since we are not concerned with the estimation of theinteger delay, in the following we set η = 0.

2.2. Signal model

We consider a linearly modulated digital signal transmittedover an AWGN channel. The complex envelope of the re-ceived waveform is modeled as

r(t) = e j(2π fdt+ϕ)s(t − εT) +w(t), (2)

where s(t) is the useful signal, ϕ and fd are the carrier phaseand frequency offset, respectively, and w(t) is thermal noisewith independent real and imaginary components, each with

M. Morelli and A. A. D’Amico 3

Burst#1 Burst#2 Burst#K

· · ·

Guardinterval

Sync.preamble UW

Header Payload

Figure 1: Burst structure.

Sync.preamble

UW Payload

τ NT

Figure 2: Start of burst estimation error.

two-sided power spectral density N0. Signal s(t) is expressedas

s(t) =∑

n

ang(t − nT), (3)

where {an} are modulation symbols taken from a PSK orQAM constellation and g(t) has a root-raised-cosine Fouriertransform with some roll-off α. To facilitate the timing esti-mation process, during the preamble we assume a pilot pat-tern composed by alternating BPSK symbols +1 and−1 [17].Accordingly, s(t) is given by

s(t) =√

2EsT

cos(πt

T

)(4)

with Es denoting the signal energy per symbol interval, andr(t) may be rewritten in the form

r(t) =√

2EsTe j(2π fdt+ϕ) cos

[π(t − εT)

T

]+w(t)

for t ∈ [0,NT].

(5)

In order to produce a discrete-time signal, the receivedwaveform is fed to an anti-aliasing filter (AAF) and sampledat some rate fc. The filter bandwidth BAAF and the samplingrate are chosen such that the signal component is passedundistorted (even for the maximum frequency offset) and noaliasing occurs. Assuming that the CFO is less in magnitudethan 0.5/T , from (5) it follows that we can set BAAF = 1/Tand fc = 2/T . For simplicity, in the ensuing discussion theAAF is assumed with a brick-wall transfer function, eventhough the rectangular shape is not strictly necessary andcould be easily made more realistic [18].

For normalization purposes, the output of the AAF isscaled by a factor

√T/2Es and we call x(k) the correspond-

ing samples taken at t = kT/2, with 0 ≤ k ≤ 2N − 1. As thesignal is not distorted in passing through the filter, we have

x(k)=e j(πkν+ϕ) cos[(

k

2−ε)π]

+ n(k) for 0 ≤ k ≤ 2N − 1,

(6)

where ν = fdT is the CFO normalized to the symbol-rate 1/Tand n(k) = nR(k) + jnI(k) is the noise contribution. Due tothe previous hypotheses, {nR(k)} and {nI(k)} are indepen-dent and white random sequences with the same varianceσ2 = (Es/N0)−1. As the signal component in (6) depends onν, ε, and ϕ, we may estimate all these parameters from theobservation of {x(k)}. This problem is addressed in the nextsection by resorting to ML methods.

3. MAXIMUM LIKELIHOOD ESTIMATION OFTHE SYNCHRONIZATION PARAMETERS

3.1. Maximization of the likelihood function

Bearing in mind (6), the log-likelihood function for the un-known parameters is given by

Λ(ν, ε, ϕ) = −2N ln(2πσ2)

− 12σ2

2N−1∑

k=0

∣∣∣∣x(k)− e j(πkν+ϕ) cos[(

k

2− ε)π]∣∣∣∣

2

,

(7)

where ν, ε, and ϕ are trial values of ν, ε, and ϕ, respec-tively. The joint ML estimate of (ν, ε,ϕ) is the location whereΛ(ν, ε, ϕ) achieves its global maximum. Skipping irrelevantfactors and additive terms independent of (ν, ε, ϕ), it turnsout that Λ(ν, ε, ϕ) may equivalently be replaced by

Ψ(ν, ε, ϕ) = �e

{e− jϕ

2N−1∑

k=0

x(k)e− jπkν cos[(

k

2− ε)π]}

,

(8)

where �e{·} denotes the real part of the enclosed quantity.Function Ψ(ν, ε, ϕ) can also be rewritten as

Ψ(ν, ε, ϕ) = �e{e− jϕ

[Ye(ν) cos(πε) + e− jπνYo(ν) sin(πε)

]}

(9)


with

Ye(ν) =N−1∑

k=0

(−1)kx(2k)e− j2πkν,

Yo(ν) =N−1∑

k=0

(−1)kx(2k + 1)e− j2πkν.

(10)

To ease the search for the maximum of Ψ(ν, ε, ϕ), we rewrite(9) in the form

Ψ(ν, ε, ϕ) = ∣∣Z(ν, ε)∣∣ cos

[ψ(ν, ε)− ϕ], (11)

where Z(ν, ε) is a function of ν and ε defined as

Z(ν, ε) = Ye(ν) cos(πε) + e− jπνYo(ν) sin(πε) (12)

while ψ(ν, ε) = arg{Z(ν, ε)} is the argument of Z(ν, ε).Clearly, for fixed ν and ε, the maximum of Ψ(ν, ε, ϕ) isachieved when the cosine factor in (11) is equal to unity,which occurs for

ϕ(ν, ε) = arg{Z(ν, ε)

}. (13)

In this case the right-hand side of (11) reduces to |Z(ν, ε)|and the ML estimates of ν and ε are found by maximizing thefollowing function:

Γ(ν, ε) = 2∣∣Z(ν, ε)

∣∣2(14)

with respect to ν and ε, where the factor 2 in the right-handside of (14) has only been inserted to avoid a factor 1/2 in thesubsequent equations.

To proceed further, we substitute (12) into (14) and ob-tain

Γ(ν, ε) = ∣∣Ye(ν)∣∣2

+∣∣Yo(ν)

∣∣2+�e

{e− j2πεA(ν)

}, (15)

where A(ν) is defined as

A(ν) = ∣∣Ye(ν)∣∣2 − ∣∣Yo(ν)

∣∣2+ 2 j�e

{e jπνYe(ν)Y∗o (ν)

}.

(16)

Observing that |A(ν)| = |Y 2e (ν) + e− j2πνY 2

o (ν)|, we mayrewrite (15) into the equivalent form

Γ(ν, ε) = ∣∣Ye(ν)∣∣2

+∣∣Yo(ν)

∣∣2

+∣∣Y 2

e (ν) + e− j2πνY 2o (ν)

∣∣ cos[θ(ν)− 2πε

] (17)

with θ(ν) = arg{A(ν)}. For a given ν, the maximum of Γ(ν, ε)is achieved by setting

ε(ν) = 12π

arg{A(ν)

}. (18)

Substituting this result into the right-hand side of (17) yields

P(ν) = ∣∣Ye(ν)∣∣2

+∣∣Yo(ν)

∣∣2+∣∣Y 2

e (ν) + e− j2πνY 2o (ν)

∣∣(19)

0.50.40.30.20.10−0.1−0.2−0.3−0.4−0.5

ν

0

0.2

0.4

0.6

0.8

1

1.2

P(ν

)

Es/N0 = 10 dBN = 64

Figure 3: Typical shape of P(ν).

from which it follows that the ML estimate of the frequencyoffset is given by

ν = arg maxν

{P(ν)

}(20)

while the timing estimate is obtained from (18) in the form

ε = 12π

arg{A(ν)

}. (21)

In case of coherent detection, an estimate of the carrier phaseϕ is also necessary. This is computed as indicated in (13) afterreplacing (ν, ε) by (ν, ε) and reads

ϕ = arg{Ye(ν) cos(πε) + e− jπνYo(ν) sin(πε)

}. (22)

In the sequel the algorithm based on (20)–(22) is calledthe ML estimator (MLE).

3.2. Remarks

(1) Contrarily to what one might fear, the maximization ofthe likelihood function Λ(ν, ε, ϕ) needs not be made on athree-dimensional domain. Actually, the location (ν, ε, ϕ) ofthe maximum can be found through simple steps, each in-volving a single synchronization parameter. In particular, thefirst step requires maximizing the function P(ν) defined in(19) in order to get the CFO estimate ν. As discussed later,this can be done through a grid search over the interval whereν is expected to lie. Once ν has been obtained, timing andphase estimates are computed in closed form as indicatedin (21) and (22), respectively. In summary, the difficult andtime-consuming part in the estimation of (ν, ε,ϕ) is the onethat locates the maximum of P(ν). Once this is done, thecomputation of ε and ϕ becomes a trivial task.

(2) Maximizing function P(ν) may pose some difficultydue to the presence of many local maxima. This is clearly ev-ident from Figure 3, which illustrates a typical realization of


P(ν) as obtained by simulation with N = 64, Es/N0 = 10 dB,and ν = 0.1. As discussed in [10], the global maximum canbe sought in two steps. The first one (coarse search) calculatesP(ν) for a set of ν values, say {νn}, covering the uncertaintyrange of ν and determines the location νM of the maximumover this set. The second step (fine search) makes an inter-polation between the samples P(νn) and computes the localmaximum nearest to νM . It should be noted that the shapeof P(ν) is occasionally so badly distorted by noise that itshighest peak may be far from the true ν. When this happens,the MLE makes large errors (outliers) and the system perfor-mance is highly degraded. The SNR below which the outliersstart to occur is referred to as the threshold of the estimator.

(3) In practice the coarse search can be efficiently per-formed using fast Fourier transform (FFT) techniques, as itis now explained. Starting from the observed samples {x(k)},we first compute the following zero-padded sequences oflength KN :

ye(k) =⎧⎨⎩

(−1)kx(2k), 0 ≤ k ≤ N − 1,

0, N ≤ k ≤ NK − 1,

yo(k) =⎧⎨⎩

(−1)kx(2k + 1), 0 ≤ k ≤ N − 1,

0, N ≤ k ≤ KN − 1,

(23)

whereK is a design parameter called pruning factor. Next, theFFTs of {ye(k)} and {yo(k)} are evaluated at the points

νn = n

KN, −KN

2≤ n ≤ KN

2. (24)

This produces the quantities {Ye(νn)} and {Yo(νn)}, whichare next exploited to get {P(νn)} as indicated in (19). Finally,the largest P(νn) is sought and this provides the coarse fre-quency estimate.

(4) Collecting (10) and (19), it is seen that P(ν) is peri-odic of unit period. This means that MLE gives unambigu-ous frequency estimates as long as ν is confined within theinterval [−1/2, 1/2). This is the frequency estimation range ofMLE.

(5) Compared to the R&B algorithm [10], the MLE ismore complex to implement as it requires the computationof two FFTs instead of a single FFT. In addition to carrier syn-chronization, however, the MLE also provides timing recov-ery. Actually, from (16) and (21) we see that computing thetiming estimate only requires knowledge of Ye(ν) and Yo(ν).Since these quantities can easily be obtained by {Ye(νn)} and{Yo(νn)} through interpolation, the timing estimation task isaccomplished with a relatively low computational effort onceν is available. However, it should be observed that the com-plexity associated to the synchronization process is negligiblecompared to that of iterative data decoding [19]. So, the re-quirement for an additional FFT has only a marginal impacton the overall receiver complexity.

4. CRB ANALYSIS

By invoking the asymptotic efficiency property of the MLE,we expect that the accuracy of the estimates (20)–(22) ap-proaches the corresponding CRBs for relatively large values

of N and Es/N0. For this reason, it is of interest to derivethe CRB for the joint estimation of the set of parametersη = (ν, ε,ϕ) based on the model (6).

We begin by computing the entries of the Fisher infor-mation matrix F. They are defined as [20]

[F]i, j = −E{∂2Λ(η)∂ηi∂ηj

}, 1 ≤ i, j ≤ 3, (25)

where Λ(η) is the log-likelihood function in (7) and η� de-notes the �th entry of η. Substituting (7) into (25), after somemanipulations we obtain

F = N

6σ2

⎡⎢⎢⎣

π2(2N−1)[4N−1−3 cos(2πε)

]0 3π

[2N−1−cos(2πε)

]

0 6π2 0

3π[2N−1−cos(2πε)

]0 6

⎤⎥⎥⎦ .

(26)

The CRB for the estimation of η� is given by [F−1]�,� . Skip-ping the details, it is found that

CRB(ν) = 12(Es/N0

)−1

π2N[4N2 − 4 + 3 sin2(2πε)

] , (27)

CRB(ε) =(Es/N0

)−1

π2N, (28)

CRB(ϕ) = 2(2N − 1)(4N − 1− 3 cos ε)

(Es/N0

)−1

N[4N2 − 4 + 3 sin2(2πε)

] . (29)

Interestingly, for large data records we can approximate (27)as

CRB(ν) ≈ 3(Es/N0)−1

π2N3(30)

which represents the CRB for the estimation of the frequencyof a complex sinusoid embedded in AWGN [10].

5. SIMULATION RESULTS

In this section we report on simulation results illustrating theperformance of MLE over an AWGN channel. Unless other-wise specified, the synchronization parameters vary at eachnew simulation run and are modeled as statistically indepen-dent random variables with a uniform distribution. In par-ticular, ν and ε are confined within [−0.5, 0.5) while ϕ takesvalues in the interval [−π,π). A pruning factor K = 4 isused to compute the quantities {Ye(νn)} and {Yo(νn)}. Also,a parabolic interpolation is chosen in the implementation ofthe fine search. This yields a frequency estimate in the form

ν = νM +δν

2· P

(νM−1

)− P(νM+1)

P(νM−1

)− 2P(νM) + P(νM+1

) , (31)

where δν = 1/KN is the distance between two adjacent sam-ples P(νn) while νM is the output of the coarse search. Theobservation length is fixed to either N = 32 or 64. Forcomparison, in the ensuing discussion we also consider asynchronization scheme in which timing recovery is first ac-complished by resorting to the Oerder and Meyr (O&M)


0.50.40.30.20.10−0.1−0.2−0.3−0.4−0.5

ν

−0.5

−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

0.3

0.4

0.5

E{ν}

E{ν} = ν

Es/N0 = 10 dBN = 64

Figure 4: Mean normalized frequency estimates versus ν.

0.50.40.30.20.10−0.1−0.2−0.3−0.4−0.5

ε

−0.5

−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

0.3

0.4

0.5

E{ε}

E{ε} = ε

Es/N0 = 10 dBN = 64

Figure 5: Mean timing phase estimates versus ε.

algorithm [8] and carrier synchronization is next achievedby applying the R&B method [10] to the time-synchronizedsamples. The O&M operates with four samples per symbolperiod.

Figures 4 and 5 illustrate average frequency and timingestimates, E{ν} and E{ε}, provided by MLE as a function ofν and ε, respectively. The observation length is N = 64 whilethe SNR is fixed to Es/N0 = 10 dB. The ideal lines E{ν} = νand E{ε} = ε are indicated as references. These results showthat ν and ε are unbiased over the full range [−0.5, 0.5).

Figures 6 and 7 compare the mean square error (MSE)of the timing estimates, E{(ε − ε)2}, as obtained with MLEand O&M. The observation length is N = 32 in Figure 6and N = 64 in Figure 7. Marks indicate simulation resultswhile the thin solid lines are drawn to ease the reading of thegraphs. The corresponding CRBs are also shown as bench-

20151050

Es/N0 (dB)

10−5

10−4

10−3

10−2

10−1

MSE

ε

O&MMLECRB

N = 32

Figure 6: MSE performance of MLE and O&M estimator with N =32.

20151050

Es/N0 (dB)

10−5

10−4

10−3

10−2

10−1

MSE

ε

O&MMLECRB

N = 64

Figure 7: MSE performance of MLE and O&M estimator with N =64.

marks. We see that MLE has the best accuracy, especially atlow SNRs where a significant gain is observed with respectto O&M. In particular, for N = 64 the MLE is close to theCRB down to Es/N0 values of 0 dB, while O&M approachesthe bound only for Es/N0 > 10 dB. This feature of the MLE


20151050

Es/N0 (dB)

10−8

10−7

10−6

10−5

10−4

10−3

10−2

MSE

ν

R&BMLECRB

N = 64

N = 32

Figure 8: MSE performance of MLE and R&B estimator with N =32 and N = 64.

is of great importance as it makes this estimator suitable forturbo-coded modulations operating at very low SNRs.

Figure 8 illustrates the accuracy of the frequency esti-mates provided by MLE and R&B with either N = 32 or64. Again, the simulation results are compared with the rel-evant CRBs. We see that the estimation accuracy keeps closeto the CRB down to a certain value of Es/N0 that dependson the adopted scheme and observation length. If the SNRis decreased further, a rapid increase in the MSE is observed.The abscissa at which the slope of the curve starts to changeindicates the estimator threshold and is a manifestation ofthe occurrence of outliers. Since large errors have disablingeffects on the system performance, the frequency estimatormust operate above threshold. The results in Figure 8 re-veal that MLE has a lower threshold than R&B, especially forN = 64, which translates into an increased robustness againstoutliers. This fact reinforces the idea that for low SNR ap-plications the MLE is more efficient than other conventionalsynchronization schemes. As expected, the threshold is a de-creasing function of the observation length. Actually, we seethat doubling N results into a threshold decrease of approxi-mately 3 dB with MLE, while a gain of 2 dB is observed withR&B.

As mentioned previously, in case of coherent detectionphase recovery is required in addition to frequency and tim-ing synchronization. The MSE of the phase estimates pro-vided by MLE and R&B is illustrated in Figure 9 as a func-tion of Es/N0. These results are qualitatively similar to thosein Figure 8. In particular, it turns out that both schemes ap-proach the CRB at intermediate/high SNR values, but MLEexhibits a lower threshold than R&B.

20151050

Es/N0 (dB)

10−3

10−2

10−1

100

2

468

2

468

2

468

MSE

ϕ(r

ad2)

R&BMLECRB

N = 64

N = 32

Figure 9: Mean square error MSEϕ versus Es/N0 with N = 32 andN = 64.

6. CONCLUSIONS

We have addressed the joint ML estimation of the carrier fre-quency, timing error, and carrier phase in burst-mode satel-lite transmissions. Thanks to a suitably designed pilot pat-tern composed of alternating binary symbols (which pro-duces two spectral lines at ±1/2T), the estimation processcan be divided into three separate steps, each devoted to therecovery of a single synchronization parameter. In particular,timing and phase recovery is accomplished in closed form,whereas the measurement of the frequency offset involves agrid search which represents the time-consuming part of theoverall synchronization procedure.

Comparisons have been made with a conventionalscheme in which timing recovery is accomplished in an NDAfashion and carrier synchronization is next achieved by ex-ploiting the time-synchronized samples. Computer simula-tions indicate that the proposed ML algorithm provides moreaccurate timing estimates at low SNR values. In addition, itexhibits increased robustness against the occurrence of out-liers in the frequency estimates. It is fair to say that these ad-vantages are achieved at the price of a certain increase of theprocessing load as compared to the conventional scheme.

The question of which method is better is not easilyanswered because it depends on the different weights thatmay be given to the various performance indicators, includ-ing estimation accuracy, computational complexity, and con-straints on the pilot pattern. It is likely that the choice willdepend on the specific application. For example, the pro-posed algorithm seems attractive for coded transmissions asit approaches the relevant CRBs down to very low SNRs. On


the other hand, at intermediate/high SNR values the conven-tional scheme is preferable as it achieves similar performancewith reduced complexity.

REFERENCES

[1] U. Mengali and A. N. D’Andrea, Synchronization Techniquesfor Digital Receivers, Plenum Press, New York, NY, USA, 1997.

[2] H. Meyr, M. Moeneclaey, and S. Fechtel, Digital Communica-tion Receivers: Synchronization, Channel Estimation, and SignalProcessing, John Wiley & Sons, New York, NY, USA, 1997.

[3] K. H. Mueller and M. Muller, “Timing recovery in digital syn-chronous data receivers,” IEEE Transactions on Communica-tions, vol. 24, no. 5, pp. 516–531, 1976.

[4] F. M. Gardner, “A BPSK/QPSK timing-error detector for sam-pled receivers,” IEEE Transactions on Communications, vol. 34,no. 5, pp. 423–429, 1986.

[5] A. N. D’Andrea and M. Luise, “Optimization of symbol timingrecovery for QAM data demodulators,” IEEE Transactions onCommunications, vol. 44, no. 3, pp. 399–406, 1996.

[6] A. A. D’Amico, A. N. D’Andrea, and R. Reggiannini, “Efficientnon-data-aided carrier and clock recovery for satellite DVB atvery low signal-to-noise ratios,” IEEE Journal on Selected Areasin Communications, vol. 19, no. 12, pp. 2320–2330, 2001.

[7] M. Moeneclaey and G. de Jonghe, “Tracking perfor-mance comparison of two feedforward ML-oriented carrier-independent NDA symbol synchronizers,” IEEE Transactionson Communications, vol. 40, no. 9, pp. 1423–1425, 1992.

[8] M. Oerder and H. Meyr, “Digital filter and square timing re-covery,” IEEE Transactions on Communications, vol. 36, no. 5,pp. 605–612, 1988.

[9] E. Panayirci and E. K. Bar-Ness, “A new approach for evaluat-ing the performance of a symbol timing recovery system em-ploying a general type of nonlinearity,” IEEE Transactions onCommunications, vol. 44, no. 1, pp. 29–33, 1996.

[10] D. C. Rife and R. R. Boorstyn, “Single-tone parameter estima-tion from discrete-time observations,” IEEE Transactions onInformation Theory, vol. 20, no. 5, pp. 591–598, 1974.

[11] D.-K. Hong and S.-J. Kang, “Joint frequency offset and car-rier phase estimation for the return channel for digital videobroadcasting,” IEEE Transactions on Broadcasting, vol. 51,no. 4, pp. 543–550, 2005.

[12] M. P. Fitz, “Planar filtered techniques for burst mode carriersynchronization,” in Proceedings of IEEE Global Telecommuni-cations Conference and Exhibition (GLOBECOM ’91), vol. 1,pp. 365–369, Phoenix, Ariz, USA, December 1991.

[13] B. C. Lovell and R. C. Williamson, “The statistical perfor-mance of some instantaneous frequency estimators,” IEEETransactions on Signal Processing, vol. 40, no. 7, pp. 1708–1723,1992.

[14] M. Luise and R. Reggiannini, “Carrier frequency recoveryin all-digital modems for burst-mode transmissions,” IEEETransactions on Communications, vol. 43, no. 234, pp. 1169–1178, 1995.

[15] U. Mengali and M. Morelli, “Data-aided frequency estimationfor burst digital transmission,” IEEE Transactions on Commu-nications, vol. 45, no. 1, pp. 23–25, 1997.

[16] Y. Fan and P. Chakravarthi, “Joint carrier phase and symboltiming synchronization for burst satellite communications,” inProceedings of the 21st Century Military Communications Con-ference (MILCOM ’00), vol. 2, pp. 1104–1108, Los Angeles,Calif, USA, October 2000.

[17] Y. Jiang, F.-W. Sun, and J. S. Baras, “On the performance limitsof data-aided synchronization,” IEEE Transactions on Informa-tion Theory, vol. 49, no. 1, pp. 191–203, 2003.

[18] H. Meyr, M. Oerder, and A. Polydoros, “On sampling rate,analog prefiltering, and sufficient statistics for digital re-ceivers,” IEEE Transactions on Communications, vol. 42, no. 12,pp. 3208–3214, 1994.

[19] S. Benedetto, R. Garello, G. Montorsi, et al., “MHOMS: high-speed ACM modem for satellite applications,” IEEE WirelessCommunications, vol. 12, no. 2, pp. 66–77, 2005.

[20] S. M. Kay, Fundamentals of Statistical Signal Processing: Estima-tion Theory, Prentice-Hall, Englewood Cliffs, NJ, USA, 1993.


Research ArticleBurst Format Design for Optimum JointEstimation of Doppler-Shift and Doppler-Ratein Packet Satellite Communications

Luca Giugno,1 Francesca Zanier,2 and Marco Luise2

1 Wiser S.r.l.–Wireless Systems Engineering and Research, Via Fiume 23, 57123 Livorno, Italy2 Dipartimento di Ingegneria dell’Informazione, University of Pisa, Via Caruso 16, 56122 Pisa, Italy

Received 1 September 2006; Accepted 10 February 2007

Recommended by Anton Donner

This paper considers the problem of optimizing the burst format of packet transmission to perform enhanced-accuracy estimationof Doppler-shift and Doppler-rate of the carrier of the received signal, due to relative motion between the transmitter and thereceiver. Two novel burst formats that minimize the Doppler-shift and the Doppler-rate Cramer-Rao bounds (CRBs) for the jointestimation of carrier phase/Doppler-shift and of the Doppler-rate are derived, and a data-aided (DA) estimation algorithm suitablefor each optimal burst format is presented. Performance of the newly derived estimators is evaluated by analysis and by simulation,showing that such algorithms attain their relevant CRBs with very low complexity, so that they can be directly embedded into new-generation digital modems for satellite communications at low SNR.

Copyright © 2007 Luca Giugno et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1. INTRODUCTION

Packet transmission of digital data is nowadays adoptedin several wireless communications systems such as satel-lite time-division multiple access (TDMA) and terrestrialmobile cellular radio. In those scenarios, the received sig-nal may suffer from significant time-varying Doppler dis-tortion due to relative motion between the transmitter andthe receiver. This occurs, for instance, in the last-generationmobile-satellite communication systems based on a con-stellation of nongeostationary low-earth-orbit (LEO) satel-lites [1] and in millimeter-wave mobile communications fortraffic control and assistance [2]. In such situations, car-rier Doppler-shift and Doppler-rate estimation must be per-formed at the receiver for correct demodulation of the re-ceived signal.

A number of efficient digital signal processing (DSP) al-gorithms have already been developed for the estimation ofthe Doppler-shift affecting the received carrier [3] and a fewalgorithms for Doppler-rate estimation are also available inthe open literature [4, 5]. The issue of joint Doppler-shiftand Doppler-rate estimation has been addressed as well, al-though to a lesser extent [6, 7]. In all the papers above, theobserved signal is either an unmodulated carrier, or con-

tains pilot symbols known at the receiver. The most commonburst format is the conventional preamble-payload arrange-ment, wherein all pilots are consecutive and they are placedat the beginning of the data burst. Other formats are the mi-damble as in the GSM system [8], wherein the preamble ismoved to the center of the burst, or the so-called pilot sym-bol assisted modulation (PSAM) paradigm [9], where theset of pilot symbols is regularly multiplexed with data sym-bols in a given ratio (the so-called burst overhead). Data-aided (DA) algorithms, which exploit the information con-tained in the pilot symbols, are routinely used to attain goodperformance with small burst overhead. The recent intro-duction of efficient channel coding with iterative detection[10] has also placed new and more stringent requirementsfor receiver synchronization on satellite modems. The car-rier synchronizer is requested to operate at a lower signal-to-noise ratio (SNR) than it used to be with conventional coding[11].

Therefore, it makes sense to search for the ultimate ac-curacy that can be attained by carrier synchronizers. It turnsout that the Cramer-Rao bounds (CRBs) for joint estima-tions are functions of the location of the reference symbolsin the burst. The issue to find the optimal burst format thatminimizes the frequency CRB has been already addressed in


a

b

N/2 N/2

N/3 N/3N/3

M

-2P format-

-3P format-

Preamble Payload Postamble

M + N/2

M/2 M/2

Payload Payload

L

P P P

c

d

N/4 M/3 N/4 N/4M/3 N/4 M/3

-1st 2P subburst- -2nd 2P subburst-

-4P format-

P Payload Payload PayloadP P P

2M/3 + N/2

Payload Payload

L

P P PP

Figure 1: 2P burst format, 3P burst format, and 4P burst format.

[12–14], but only for joint carrier phase/Doppler-shift es-timation. The novelty of the paper is to extend the anal-ysis to the joint carrier phase/Doppler-shift and Doppler-rate estimation. It is known [12–15] that the preamble-postamble format (2P format) described in the sequel min-imizes the frequency CRB with no Doppler-rate, and withconstraints on the total training block length and on theburst overhead of the signal. We demonstrate here that suchformat is optimal in the presence of Doppler-rate as well,and that the Doppler-rate CRB is minimized by estima-tion over three equal-length blocks of reference symbols thatare equally spaced by data symbols (3P format). We alsoshow that other formats are very close to optimality (4P for-mat).

In addition to computation of the burst, we also in-troduce new high-resolution and low-complexity carrierDoppler-shift and Doppler-rate DA estimation algorithmsfor such optimal burst formats.

The paper is organized as follows. In Section 2, wefirst outline the received signal model affected by Dopplerdistortions. Next, in Section 3 we present and analyze alow-complexity DA Doppler-shift estimator for the optimal2P format. Extensions of this algorithm for joint carrierphase/Doppler-shift and Doppler-rate estimation for the 2Pformat, the 3P format, and the sub-optimum 4P format, areintroduced in Sections 4 and 5, respectively. Finally, someconclusions are drawn in Section 6.

2. SIGNAL MODEL

In this paper, we take into consideration three different databurst formats as depicted in Figure 1.

In all cases, the total number of pilot symbols that areknown to the receiver is equal to N , and the total length ofthe “data payload” fields that contain information symbols isequal to M. The formats differ for the specific pilots arrange-ment in two/three/four groups of N/2, N/3, N/4 consecutivepilot symbols equally spaced by data symbols. Hereafter wewill address them as “2P,” “3P,” “4P” formats as in Figures1(a), 1(b), 1(c), respectively. We denote also with L = N +Mthe overall burst length, and with η the burst overhead, thatis, the ratio between the total number of pilot symbols and

the total number of symbols within the burst:

η = N

L= N

N + M= 1

1 + M/N. (1)

We also assume BPSK/QPSK data modulation for the pilotfields, and additive white Gaussian noise (AWGN) channelwith no multipath. Filtering is evenly split between transmit-ter and receiver, and the overall channel response is Nyquist.Timing recovery is ideal but the received signal is affected bytime-varying Doppler distortion. Filtering the received wave-form with a matched filter and sampling at symbol rate atthe zero intersymbol interference instants yields the follow-ing discrete-time signal:

z(k) = ckejϕk + n(k), k = −L− 1

2, . . . , 0, . . . ,

L− 12

,

(2)

where

ϕk = θ + 2πνkT + παk2T2 (3)

is the instantaneous carrier excess phase, {ck} are unit-energy(QPSK) data symbols and L (odd) is the observation (burst)length. Also, 1/T is the symbol rate, θ is the unknown initialcarrier phase, ν is the constant unknown carrier frequencyoffset (Doppler-shift), and finally α is the constant unknowncarrier frequency rate-of-change (Doppler-rate). For signalmodel (2) to be valid, we assumed that the value of theDoppler-shift ν is much smaller than the symbol rate, andthat the value of the Doppler-rate α is much smaller thanthe square of the symbol rate. The noise n(k) is a complex-valued zero-mean WGN process with independent compo-nents, each with variance σ2 = N0/(2Es), where Es/N0 repre-sents the ratio between the received energy-per-symbol andthe one-sided channel noise power spectral density.

Estimation of ν and α from the received signal z(k) re-quires preliminary modulation removal from the pilot fields.Broadly speaking, it is customary to adopt BPSK or QPSKmodulation for pilot fields, so that modulation removal iseasily carried out by letting r(k) = c∗k z(k). The result is

r(k) = e jϕk + w(k), k ∈K ={⋃

NPi

}, (4)

Luca Giugno et al. 3

where K is the symmetric set of N time indices correspond-ing to pilot symbols, and w(k) = c∗k n(k) is statistically equiv-alent to n(k). We explicitly mention here that we have cho-sen a symmetrical range K with respect to the middle ofthe burst since such arrangement decouples the estimationof some parameters, as discussed in [12] and in Appendix B.The signal r(k) will be considered from now on as our ob-served signal that allows to carry out the carrier synchro-nization functions. We show in Appendix B that the burstformats in Figure 1 are optimum so far as the estimation ofparameters ν and α is concerned. To keep complexity low, wewill not take into consideration here “mixed,” partially blind,methods to perform carrier synchronization that use both theknown pilot symbols and all of the intermediate data sym-bols of the burst, like envisaged in [16] for the case of channelestimation.

3. DOPPLER-SHIFT ESTIMATOR: FEPE ALGORITHM

We momentarily neglect the effect of the Doppler-rate α in(4), to concentrate on the issue of Doppler-shift estimationonly. Under such hypothesis, (4) can be rewritten as follows:

r(k) = e j(θ+2πνkT) + w(k), k ∈ K. (5)

The 2P format minimizes the CRB for Doppler-shift esti-mation for joint carrier phase/Doppler-shift estimation [12–15]. Conventional frequency offset estimators for consecu-tive signal samples [3] are not directly applicable to a burstformat encompassing a preamble and a postamble. In addi-tion, straightforward solution of a maximum-likelihood es-timation problem for ν appears infeasible. We introduce thusa new low-complexity algorithm suitable for the estimationof the Doppler-shift ν in (4) with the burst format as above.The key idea of the 2P frequency estimator is really a naiveone: we start by computing two phase estimates, the one onthe preamble section, and the other on the postamble, us-ing the standard low-complexity maximum-likelihood (ML)algorithm [17]:

θ1=arg

{ −(M−1)/2∑

k=−(N+M−1)/2

r(k)

}, θ2=arg

{ (N+M−1)/2∑

k=(M−1)/2

r(k)

},

(6)

where arg{·} denotes the phase of the complex-valued ar-gument. Then we associate the two phase estimates to thetwo midpoints of the preamble and postamble sections, re-spectively, whose time distance is equal to (M + N/2)T(Figure 1(a)). After this is done, we simply derive the fre-quency estimate as the slope of the line that connects the two

points (−(M − 1)/2−N/4, θ1) and ((M − 1)/2 + N/4, θ2) onthe (time, phase) plane:

ν =∣∣∣∣θ2

∣∣2π −

∣∣θ1∣∣

2π

∣∣2π

2π(M + N/2)T. (7)

This simple algorithm is known as frequency estimationthrough phase estimation (FEPE) [15]. The operator |x|2π re-turns the value of x modulo 2π, in order to avoid phase am-biguities, and is trivial to implement when operating with

−1.5

−1

−0.5

0

0.5

1

1.5×10−3

ME

V

−1.5 −1 −0.5 0 0.5 1 1.5×10−3

νT (Hz× s)

IdealEs/N0 = 0 dBEs/N0 = 10 dB

Es/N0 = 20 dBEs/N0 = 100 dB

Figure 2: MEV of FEPE estimator for different values of ES/N0—simulation only. Preamble + postamble DA ML phase estimation,N = 44, M = 385.

fixed-point arithmetic on a digital hardware. It is easy to ver-ify that such estimator is independent of the particular ini-tial phase θ, that vanishes when computing the phase dif-ference at the numerator of (7). It is also clear that theoperating range of the estimator is quite narrow. In ordernot to have estimation ambiguities, we have to ensure that

−π ≤ |θ2|2π−|θ1|2π < π, and therefore the range is boundedto

|ν| ≤ 12(M + N/2)T

. (8)

This relatively narrow interval does not allow to use the FEPEalgorithm for initial acquisition of a large frequency offset atreceiver start-up. Its use is therefore restricted to fine esti-mation of a residual offset after a coarse acquisition or com-pensation of motion-induced Doppler-shift. Figure 2 depictsthe normalized mean estimated value (MEV) curves of theFEPE algorithm (i.e., the average estimated value E{ν} as afunction of the true Doppler-shift ν) for different values ofEs/N0 as derived by simulation. In our simulations we usethe values N = 44 and M = 385 taken from the design de-scribed in [11], so that the overhead is η = 10% (typical forshort bursts). MEV curves show that the algorithm is unbi-ased in a broad range around the true value (here, ν = 0). Itcan be shown that this is true as long as ν2NT � 1, so that

the “ancillary” estimates θ2 and θ1 are substantially unbiasedas well. Such condition is implicitly assumed in (8) since inthe practice M � N/2. The curve labeled Es/N0 = 100 dB(which is totally unrealistic) has the only purpose of showingthe bounds of the unambiguous estimation range.

It is also easy to evaluate the estimation error variance of

the FEPE estimator. It is known in fact that θ1 and θ2 in (7)have an estimation variance σ2

θthat achieves the Cramer-Rao


Bound (CRB) [17]:

σ2θ= CRB(θ) = 1

2 ·N/21

Es/N0. (9)

Therefore, considering that the two phase estimates in (7) areindependent, we get

σ2FEPE(ν)=

2 · σ2θ

4π2(M + N/2)2T2= 1

4π2T2N/2(M + N/2)2

1Es/N0

.

(10)

The vector CRB [18] for the frequency offset estimate in thejoint carrier phase/Doppler-shift estimation with the 2P for-mat is derived in Appendix A and reads as follows:

VCRB2P(ν)= 34π2T2(N/2)

[4(N/2)2 + 3M2 +3MN−1

] 1Es/N0

.

(11)

Both from the expression of the bound (11) and of thevariance (10), it is seen that the estimation accuracy has aninverse dependence on (N/2)3, and this is nothing new withrespect to conventional estimation on a preamble only. Theimportant thing is that we also have inverse dependence onM2, due to the 2P format that gives enhanced accuracy (withsmall estimation complexity) with respect to the conven-tional estimator. From (1), we also have M = N(1/η − 1),so that the term 3M2 dominates (N/2)2 as long as η < 1/2,which is always verified in the practice.

Therefore, the ratio between the CRB (11) and the vari-ance of the FEPE estimator is very close to 1. With N = 44and M = 385, we get, for instance, σ2

FEPE/VCRB2p = 0.99.The enhanced-accuracy feature is also apparent in the com-parison of the VCRB2p(ν) as in (11) with the conventionalVCRB(ν) [18] for frequency estimation on a single preamblewith length N , that is obtained by letting M = 0 in (11). Thereverse of the coin is of course the reduced operating range(8) of the estimator.

Figure 3 shows curves of the (symbol-rate-normalized)RMSEE (root mean square estimation error) of the FEPE

algorithm (i.e., T√E{(v − v)2}) as a function of Es/N0 for

various values of the true offset ν. In particular, marks aresimulation results for σ2

FEPE, whilst the lowermost line is theVCRB2p(ν). We do not report the curve for (10) since itwould be totally overlapped with (11).

Performance assessment of the FEPE estimator is con-cluded in Figure 4 with the evaluation of the sensitivity of theRMSEE to different values of an uncompensated Doppler-rate α. Just to have an idea of practical values of αT2 to be en-countered in practice, we mention that the largest Doppler-rates in LEO satellites are of the order of 200 Hz/s [1, 19] fora carrier frequency of 2.2 GHz, and assuming a symbol rateof 2 Mbaud, we end up with the value αT2 = 5.10−11. Fromsimulation results, we highlight that the performance of thisalgorithm is affected by α, but only in the case of a normal-ized Doppler-rate αT2 ≥ 10−7, that is larger than those thatare found in the practice.

Finally, the complexity of the FEPE estimator with re-spect to conventional methods of frequency estimation [3,

10−6

10−5

10−4

10−3

10−2

Nor

mal

ized

RM

SEE

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Es/N0 (dB)

σ2FEPE (ν)

νT = 1× 10−3

νT = 1× 10−4

VCRB (ν)

VCRB2P (ν)

Figure 3: RMSEE of FEPE estimator for different values ofES/N0 and relevant bounds—solid lines: theory—marks: simula-tion. Preamble + postamble DA ML phase estimation, N = 44,M = 385.

13] is presented in Table 1. It is clear that the strength of theFEPE algorithm is its very low complexity as compared toconventional algorithms.

4. DOPPLER-RATE ESTIMATORS IN 2P FRAME:FREPE AND FREFE ALGORITHMS

We take now back into consideration the presence of a non-negligible Doppler-rate in the received signal, modeled as in(3)-(4). We focus again on the 2P format (Figure 1(a)), sinceit is the optimal format for Doppler-shift estimation in jointcarrier phase/Doppler-shift and Doppler-rate estimation too,as demonstrated in Appendix B. A new simple estimator forα in the 2P format is found by a straightforward general-ization of the FEPE approach. Assume that we further splitboth the preamble and the postamble into two subsections ofequal length, and we compute four (independent) ML phaseestimates on the two subsections. We know in advance thatthe time evolution of the phase is described by a parabola.The four phase estimates can thus be used to fit a second-order phase polynomial according to the Minimum MeanSquared Error (MMSE) criterion; taking the origin in the


10−6

2

3

4567

10−5

2

3

4567

10−4

2

3

4567

10−3

Nor

mal

ized

RM

SEE

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Es/N0 (dB)

VCRB2P (ν)αT2 = 0αT2 = 2× 10−8

αT2 = 5× 10−8

αT2 = 1× 10−7

αT2 = 2× 10−7

αT2 = 2.5× 10−7

Figure 4: Sensitivity of FEPE estimator to different values of theDoppler-rate αT2. Preamble + postamble DA ML phase estimation,N = 44, M = 385, vT = 1.0× 10−3.

first section of the preamble, we obtain the phase model

ϕP(n) = aπ(n +

M − 12

+3N8

)2

+ 2πb(n +

M − 12

+3N8

)+ c,

(12)

where the regression coefficients a and b directly repre-sent estimates for the (normalized) carrier Doppler-rate andDoppler-shift, respectively, and c is an estimate for the initialphase (that we are not interested into). The coefficients arefound after observing that the MSE is written as

ε(a, b, c) =4∑

i=1

[ϕP(ni)− θi

]2 =4∑

i=1

e2i , (13)

where θi, i = 1, . . . , 4, are the above-mentioned ML phaseestimates on N/4 pilots each, and n1 = −[(M−1)/2 + 3N/8],n2 = −[(M − 1)/2 + N/8], n3 = [(M − 1)/2 + N/8], andn4 = [(M − 1)/2 + 3N/8] are the four time instants that weconventionally associate to the four estimates (the midpointsof the four subsections). Equating to zero the derivatives of

Table 1: The FEPE computational complexity comparison.(Nalg = estimation design parameter.)

Computational complexity of majorDoppler-shift estimation algorithms

Algorithm ReferenceNumber of real productsand additions

LUT access

L&R [3] 4N(Nalg + 1

)− 2 1

M&M [3] Nalg(8N − 4Nalg − 3

)− 2 Nalg

S-BLUE [13] 4N2 + 4.5N − 3 1.5N − 2

P-BLUE-2 [13] 4N − 1 1

FEPE — 2N + 3 2

ε(a, b, c) with respect to a, b, and c, we obtain

∂ε(a, b, c)∂a

=4∑

i=1

ei ·[ni +

(M − 1

2+

3N8

)]2

= 0,

∂ε(a, b, c)∂b

=4∑

i=1

ei ·[ni +

(M − 1

2+

3N8

)]= 0,

∂ε(a, b, c)∂c

=4∑

i=1

ei = 0,

(14)

and solving for a we get the following so-called frequency rateestimation through phase estimation (FREPE) algorithm [15]:

αFREPE = a

T2=(θ4 − θ3

)− (θ2 − θ1)

πN/2(N/2 + M)T2(15)

(all differences to be intended modulo-2π). This extremelysimple approach can be viewed as a generalization of theFEPE introduced in the previous section. In particular, by us-ing (7), the terms

(θi − θi−1

)

2π(N/4)T, i = 2, 4, (16)

represent two Doppler-shift estimations, the first on thepreamble and the second on the postamble, respectively,which are spaced M + N/2 symbols apart. The Doppler-rateestimate is thus simply the difference between the two fre-quency estimates, divided by their time distance (M+N/2)T .

The considerations above allow us to also introducethe frequency rate estimation through frequency estimation(FREFE) algorithm [15]

αFREFE = ν2 − ν1

(M + N/2)T, (17)

wherein the two frequency estimates ν1 and ν2 can be ob-tained by any conventional algorithm [3] operating sepa-rately on the preamble and on the postamble, respectively.We can choose for instance the L&R algorithm [20] or theR&B algorithm [21]. Assuming that the selected algorithmoperates close enough to the CRB (as is shown in [3]), the


variance of (17) is

σ2FREFE(α) = 2σ2

ν

(M + N/2)2T2

= 3π2T4N/2

((N/2)2 − 1

)(M + N/2)2

1Es/N0

,

(18)

where we have used σ2ν = 3 · (Es/N0)−1/[2π2T2N/2((N/2)2 −

1)] [17]. This can be compared to the variance of the FREPEalgorithm that is easily found to be

σ2FREPE(α) =

4 · σ2θ

π2(N/2)2(M + N/2)2T4

= 4π2T4(N/2)3(M + N/2)2

1Es/N0

,

(19)

where now σ2θ= (Es/N0)−1/(N/2). The relevant vector CRB

for Doppler-rate estimate is (see Appendix B):

VCRB2P(α)

= 45π2T4

((N/2)3−N/2)(16(N/2)2 +15M2 +30MN/2−4

) 1Es/N0

.

(20)

All expressions inversely depend on (N/2)5 as in conven-tional preamble-only estimation of the Doppler-rate [6], butthey also bear again inverse dependence on M2 that gives en-hanced accuracy. For sufficiently large values of N and M,M� N , we have

σ2FREFE(α)σ2

FREPE(α)∼= 3

4,

VCRBPP(α)σ2

FREFE(α)∼= 1. (21)

Figure 5 shows the MEV curves (i.e., E{α}) of the FREPE al-gorithm for different values of Es/N0, in the case of N = 44,M = 385, and Doppler-shift vT = 10−3. The estimator isunbiased with an operating range equal to

∣∣αFREPE∣∣ ≤ 1

N/2(M + N/2)T2. (22)

The sensitivity of FREPE to different uncompensated val-ues of vT is illustrated in Figure 6 in terms of MEV.

The same simulations have been run also for the FREFEalgorithm. In particular, Figure 7 illustrates the MEV curvesfor different values of Es/N0 and with vT = 10−3. By usingthe L&R algorithm to estimate ν1 and ν2, the operating rangeof FREFE is roughly twice that of FREPE:

∣∣αFREFE∣∣ ≤ 1

(N/4 + 1)(M + N/2)T2. (23)

In particular, the term [(N/2 + 1)T]−1 represents the fre-quency pull-in range of L&R on N/2 pilots [20].

Figure 8 demonstrates that FREPE is also less sensitivethan FREFE to an uncompensated Doppler-shift. Finally,Figure 9 shows the curve of the Doppler-rate RMSEE ofFREPE and FREFE as a function of Es/N0, for νT = 10−3 andαT2 = 10−6. The FREPE estimator loses only 10 log10(4/3) =1.25 dB in terms of Es/N0 with respect to the performance ofthe more complex FREFE when N � 1.

−1.5

−1

−0.5

0

0.5

1

1.5×10−4

ME

V

−1.5 −1 −0.5 0 0.5 1 1.5×10−4

αT2 (Hz/s× s2)


Es/N0 = 20 dBEs/N0 = 100 dB

Figure 5: MEV of FREPE estimator for different values of ES/N0—simulation only. Preamble + postamble DA ML phase estimation,N = 44, M = 385, vT = 1.0× 10−3.

−1.5

−1

−0.5

0

0.5

1

1.5×10−4

ME

V

−1.5 −1 −0.5 0 0.5 1 1.5×10−4

αT2 (Hz/s× s2)

IdealνT = 0νT = 1× 10−3

νT = 5× 10−3

νT = 1× 10−2

Figure 6: MEV of FREPE estimator for different values of theDoppler-shift vT—simulation only. Preamble + postamble DA MLphase estimation, N = 44, M = 385, Es/N0 = 10 dB.

5. OPTIMUM DOPPLER-RATE ESTIMATION

5.1. Odd number of pilot fields: FRE-3PE algorithm

We turn now to the issue of optimum burst configurationfor the estimation of the Doppler-rate. We demonstrate inAppendix B that the 3P format (Figure 1(b)) minimizes theCRB for Doppler-rate estimation, with the usual constraintson the total training block length and on the burst over-head (1). In the following, we develop a new low-complexityalgorithm suitable for Doppler-rate estimation with the 3Pformat. We know in advance that the time evolution of thephase is described by a parabola. As was done for the FREPE


−2.5

−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

2.5×10−4

ME

V

−2.5 −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 2.5×10−4

αT2 (Hz/s× s2)


Es/N0 = 20 dBEs/N0 = 100 dB

Figure 7: MEV of FREFE estimator for different values of ES/N0—simulation only. Preamble + postamble Luise and Reggiannini, N =44, M = 385, vT = 1.0× 10−3.

−2.5

−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

2.5×10−4

ME

V

−2.5 −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 2.5×10−4

αT2 (Hz/s× s2)

IdealνT = 0νT = 1× 10−3

νT = 5× 10−3

νT = 1× 10−2

Figure 8: MEV of FREFE estimator for different values of theDoppler-shift vT—simulation only. FREFE estimator preamble +postamble Luise and Reggiannini, N = 44, M = 385, Es/N0 =10 dB.

algorithm in the 2P configuration, a simple estimator of αin the 3P format is found by computing three (independent)ML phase estimates on the three blocks of pilots, and thenfitting a second-order phase polynomial. Taking the origin inthe first block of pilots, we obtain this time the phase model

ϕP(n) = aπ(n+

N

3+M

2

)2

+ 2πb(n+

N

3+M

2

)+ c. (24)

The coefficients are found solving the following set of equa-tions:

ϕP(ni) = θi, i = 1, . . . , 3, (25)

10−8

10−7

10−6

10−5

10−4

10−3

Nor

mal

ized

RM

SEE

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Es/N0 (dB)

FREPE, αT2 = 1× 10−6

FREFE, αT2 = 1× 10−6FRE-2FEPE, αT2 = 1× 10−6

FRE-3PE, αT2 = 1× 10−6

VCRBP (α)

VCRB2P (α)

VCRB4P (α)

VCRB3P (α)

Figure 9: RMSEE of FREPE, FREFE, FRE-3PE, and FRE-2FREPEestimators for different values of ES/N0 and relevant bounds,—solidlines: theory—marks: simulation. Doppler-rate algorithms: FREFEversus FREPE versus FRE-3PE versus FRE-2FEPE, N = 44(45),M = 385(384), vT = 1.0× 10−3.

where θi are the above-mentioned ML phase estimates onN/3 pilots each, and where n1 = −(M/2 + N/3), n2 = 0, andn3 = (M/2 + N/3) are the three time instants that we con-ventionally associate to the three estimates (the midpoints ofthe three subsections). Solving for a, we get the following so-called (FRE-3PE) (frequency rate estimation through 3 phaseestimations) algorithm:

αFRE-3PE = a

T2= 18

[(θ3 − θ2

)− (θ2 − θ1)]

π(2N + 3M − 2)2T2(26)

(all differences to be intended modulo-2π). The estimator isunbiased with an operating range equal to:

∣∣αFRE-3PE∣∣ ≤ 18

(2N + 3M − 2)2T2. (27)

In our simulations (N = 45 and M = 384), |αFRE-3PE · T2| ≤10−5. This range is narrower than FREPE’s and FREFE’s inthe 2P format, but it still widely includes practical Doppler-rate values mentioned in Section 3. Figure 10 shows the MEVcurves of the FRE-3PE algorithm for different values ofEs/N0, in the case of N = 45, M = 384, and Doppler-shift


−1.5

−1

−0.5

0

0.5

1

1.5×10−5

ME

V

−1.5 −1 −0.5 0 0.5 1 1.5×10−5

αT2 (Hz/s× s2)


Es/N0 = 20 dBEs/N0 = 100 dB

Figure 10: MEV of FRE-3PE estimator for different values ofES/N0—simulation only. 3 blocks of pilots DA ML phase estima-tion, N = 45, M = 384, vT = 1.0× 10−3.

vT = 10−4, while Figure 11 shows the sensitivity of the MEVto different uncompensated values of the Doppler-shift vT .

The theoretical error variance of the FRE-3PE estimatorcan be easily evaluated, similarly to what was done for thecalculation of σ2

FREFE(α) in Section 4:

σ2FRE-3PE(α) =

182 · 6 · σ2θ

π2(2N + 3M − 2)4T4

= 182 · 6π2T4(2N/3)(2N + 3M − 2)4

1Es/N0

,

(28)

where now σ2θ= (Es/N0)−1/(2N/3). Comparing this expres-

sion with the VCRB3P(α) in (B.11) and with the variances ofthe FREFE and FREPE algorithms, we note that all expres-sions inversely depend on N5 as in conventional preamble-only estimation of the Doppler-rate [6]. On the other hand,σ2

FRE-3PE(α) and VCRB3P(α) inversely depend on M4, out-performing the accuracy of both the traditional preamble-only format and the 2P format (that depends on M−2). Theenhanced accuracy is highlighted by Figure 9, where we re-port the simulated RMSEE (marks) of FRE-3PE, FREPE, andFREFE versus Es/N0. To perform a fair comparison, we alsoreported the VCRBP(β), obtained in the case of estimation ofDoppler-rate in the preamble-only configuration. The FRE-3PE algorithm attains its own CRB, and exhibits a gain of19 dB in terms of Es/N0 with respect to the 2P format.

As a final remark, we only mention that a simple estima-tor of Doppler-shift in the 3P format is found by applying theFEPE algorithm to the two extreme pilot fields of the burst.Its variance reaches the VCRB3P(ν) calculated setting x = 1in (B.7) and (B.9), that is 1.5 dB apart from the VCRB2P(ν)of the optimal 2P format.

−1.5

−1

−0.5

0

0.5

1

1.5×10−5

ME

V

−1.5 −1 −0.5 0 0.5 1 1.5×10−5

αT2 (Hz/s× s2)

IdealνT = 0νT = 1× 10−4

νT = 5× 10−4

νT = 1× 10−3

Figure 11: MEV of FRE-3PE estimator for different values of theDoppler-shift vT—simulation only. 3 blocks of pilots, N = 45, M =384, ES/N0 = 10 dB.

5.2. Even number of pilot fields: FRE-2FEPE algorithm

When the number of pilot fields is even, the optimum burstformat turns out to be the 4P as shown in Appendix B.We notice that the ratio of the two bounds for 3P and4P amounts to VCRB4p(α)/VCRB3p(α) ∼= 9720/108 · 640/51840 ∼= 1.09 M� N , so that 4P is only slightly optimal.

A simple estimator of α in the 4P format is found by astraightforward generalization of the FEPE and FREFE ap-proaches. Assume that we split the burst into two 2P sub-bursts of length (M/3 + N/2), (Figure 1(d)). Each preambleand postamble is now of length N/4, and we can derive twoFEPE estimates of frequency on each subburst:

ν1 =∣∣∣∣θ2

∣∣2π −

∣∣θ1∣∣

2π

∣∣2π

2π(M/3 + N/4)T, ν2 =

∣∣∣∣θ4∣∣

2π −∣∣θ3

∣∣2π

∣∣2π

2π(M/3 + N/4)T,

(29)

where θi, i = 1, . . . , 4, are the ML phase estimates computedon the four pilot fields of N/4 pilots each. The two Doppler-shift estimates ν1 and ν2 are associated with the two mid-point instants of the two 2P subbursts, whose time distanceis equal to (2M/3 + N/2)T (Figure 1(c)). Again, we estimatethe Doppler-rate as the slope of the line that connects the twopoints (−(M/3− 1/2)−N/4, ν1) and ((M/3− 1/2) +N/4, ν2)in the (time, frequency) plane:

αFRE-2FEPE = ν2 − ν1

(2M/3 + N/2)T. (30)

We call this algorithm FRE-2FEPE (frequency rate estimationthrough two FEPE estimations) .

It is clear that the operating range of the estimator withrespect to ν comes from the application of (8) to the newconfiguration and turns out to be |ν| ≤ [2(M/3 + N/4)T]−1.The MEV curves of FRE-2FEPE are not reported here since


they basically mimic those in Figures 10 and 11 for theFRE-3PE algorithm. The estimation error variance of (30)is found to be

σ2FRE-2FEPE(α) =

σ2θ

(2M/3 + N/2)2(M/3 + N/4)2π2T2

= 2 · (Es/N0)−1

π2T4N(2M/3 + N/2)2(M/3 + N/4)2.

(31)

Figure 9 shows also the curves of the RMSEE of FRE-2FEPEand its respective CRB. The FRE-2FEPE algorithm reaches itsown VCRB4p(α) and thus, as demonstrated in Appendix B, itgains 10 log10(7.19) = 18.5 dB in terms of Es/N0 with respectto the performance of the previous algorithms with the 2Pformat. Also, the FRE-2FEPE loses only 0.4 dB with respectto the FRE-3PE algorithm and can thus be a valid alternativeto the 3P format.

As a final remark, we briefly address the issue of Doppler-shift estimation in the 4P format. The best method is foundby applying the FEPE algorithm to the two extreme pilotfields of the burst. Its variance is close to the VCRB4P(ν) cal-culated setting x = 1 in (B.8) and (B.9), that is 2.4 dB worsethan the VCRB2P(ν) of the optimal 2P format.

6. CONCLUSIONS

In this paper, we presented and analyzed some very-low-complexity algorithms for carrier Doppler-shift andDoppler-rate estimation in burst digital transmission. Toachieve enhanced accuracy, the burst configurations thatminimize the CRB for the estimation of Doppler-shift andDoppler-rate are derived. Our analysis showed that the 2Pformat is optimum for Doppler-shift estimation and that the3P format is optimum for Doppler-rate estimation. Thesetwo configurations can be practically thought as repetition oftwo/three consecutive conventional (preamble-only) bursts.Despite preventing from real-time processing of the data pay-load section, the 2P and 3P formats greatly outperform theestimation based on conventional preamble-only pilot dis-tribution. Performance assessment has shown that all of theproposed algorithms are unbiased in practical operating con-ditions, and that their accuracy in terms of estimation vari-ance gets remarkably close to their respective CRBs down tovery low Es/N0 values.

APPENDICES

A. VCRB FOR JOINT CARRIER PHASE/DOPPLER-SHIFTESTIMATION WITH 2P FORMAT

In this appendix, we calculate the VCRB for the error vari-ance of any unbiased estimator of Doppler-shift in the case ofjoint estimation of phase/Doppler-shift using the preamble-postamble (2P) format. We explicitly mention that we havechosen a set K of pilot locations that is symmetrical withrespect to the middle of the burst, since a symmetrical K de-couples phase from Doppler-shift estimation, as discussed in

[12]. After modulation removal, the generic sample withinthe preamble and the postamble is given by (5).

The Fisher information matrix (FIM) [18] can be writtenas

F =[Fθθ Fθν

Fνθ Fνν

]

=

⎡⎢⎢⎢⎢⎣

−Er{∣∣∣∣∣

∂2 ln p(r | ν, θ)

∂θ2

∣∣∣∣∣

}−Er

{∣∣∣∣∣∂2 ln p(r | ν, θ)

∂θ∂ν

∣∣∣∣∣

}

−Er{∣∣∣∣∣

∂2 ln p(r | ν, θ)

∂ν∂θ

∣∣∣∣∣

}−Er

{∣∣∣∣∣∂2 ln p(r | ν, θ)

∂ν2

∣∣∣∣∣

}

⎤⎥⎥⎥⎥⎦

,

(A.1)

where p(r | ν, θ) is the probability density function of r ={r(k)}, k ∈ K , conditioned on (ν, θ), and r(k) is a randomGaussian variable with variance equal to σ2 = N0/(2Es) andmean value equal to

s(k) = e j(θ+2πνkT). (A.2)

Therefore, we write p(r | ν, θ) as

p(r | ν, θ) =∏

k∈Kp(rk | ν, θ

)

= 1(2πσ2

)N exp

{− 1

2σ2

∑

k∈K

∣∣r(k)− s(k)∣∣2}.

(A.3)

Taking the logarithm of (A.3), we obtain

ln p(r | ν, θ)

= N ln(

12πσ2

)− 1

2σ2

∑

k∈K

[∣∣r(k)∣∣2

+∣∣s(k)

∣∣2

− 2Re{r(k)s∗(k)

}]

=C +1σ2

∑

k∈KRe{r(k)s∗(k)

},

(A.4)

where C is a constant term that includes all the quantities

independent of ν and θ. After differentiating twice (A.4) with

respect to ν and θ, calculating the expectation of the variousterms with respect to r, we get

F =[a′ b′

c′ d′

], (A.5)

where

a′ =(

1σ2

) ∑

k∈K

{(1)Er

[Re{r(k)s∗(k)

}]},

b′ =(

1σ2

) ∑

k∈K

{(2πTk)Er

[Re{r(k)s∗(k)

}]},

c′ =(

1σ2

) ∑

k∈K

{(2πTk)Er

[Re{r(k)s∗(k)

}]},

d′ =(

1σ2

) ∑

k∈K

{(4π2T2k2)Er

[Re{r(k)s∗(k)

}]}.

(A.6)


By noticing that

Er[Re{r(k)s∗(k)

}] = 1, (A.7)

we obtain

F = 1σ2

⎡⎢⎢⎢⎢⎣

∑

k∈K(1) 2πT

∑

k∈Kk

2πT∑

k∈Kk 4π2T2

∑

k∈Kk2

⎤⎥⎥⎥⎥⎦

, (A.8)

where, considering the symmetry of the range K ,

∑

k∈K(1) = N ,

∑

k∈Kk = 0, (A.9)

∑

k∈Kk2 = N/2

3

[8(N

2

)2

− 6(N

2

)+ 1

+ 3M2 + 3M(

3(N

2

)− 1

)].

(A.10)

After calculation of F−1, the VCRB for ν in case of jointphase/Doppler-shift estimation is found to be

F−1νν = VCRB2P(ν) = 1

2π2T2∑

k∈K k2

1Es/N0

= 3 · (Es/N0)−1

4π2T2(N/2)[4(N/2)2 + 3M2 + 3MN − 1

] .(A.11)

B. OPTIMAL SYMMETRIC BURST CONFIGURATIONFOR JOINT CARRIER-PHASE/DOPPLER-SHIFTAND DOPPLER-RATE ESTIMATION:2P, 3P, 4P FORMATS

This appendix addresses the optimal signal design forDoppler-shift ν and Doppler-rate α estimation in the case ofjoint phase/Doppler-shift and Doppler-rate estimation whenthe received signal is expressed by (2)–(4). The optimal train-ing signal structure is developed by minimizing the vectorCramer-Rao bounds (VCRBs) [17, 18] for ν and α, withconstraints on the total training block length and on theburst overhead (1) of the signal (4). In fact, the Cramer-Raobounds (CRBs) for joint estimations are functions of the lo-cation of the reference symbols in the burst.

The issue of finding the optimal burst format that mini-mizes the frequency CRB has been already addressed in [12–14], but only for joint phase/Doppler-shift estimation. Werestrict our analysis to a symmetric burst format. In the se-quel, we demonstrate that this symmetry also decouples theestimation of Doppler-shift and Doppler-rate. Our attentionis focused on a generic burst format as in Figure 12, eitherwith an even (Figure 12(a)) or an odd (Figure 12(b)) num-ber of blocks of pilots. Just to rehearse notation, we mentionthat the length of the burst is L symbols, N is the total num-ber of pilot symbols, NP is the number of reference symbolsin each subgroup, M is the total number of data symbols,and MD is the number of data symbols in each subgroup.In Figure 12(a), 2xeven is the (even) number of subgroups of

NP MD NP MD NP MD NP MD NP MD NP

-Symmetric format-

0

P P P PP P

(a)

NP MD NP MD NP MD NP MD NP MD NP MD NP

0L

P P P P PP P

(b)

Figure 12: Generic symmetric burst format.

pilot symbols, and (2xeven + 1) is the (odd) number of sub-groups of data symbols; in Figure 12(b), (2xodd + 1) is the(odd) number of subgroups of pilot symbols, and 2xodd isthe (even) number of subgroups of data symbols. In the se-quel we find the values of x that minimize the VCRBs of νand α, for fixed values of L, N , and M.

In the case of joint phase/Doppler-shift/Doppler-rate es-timation, the fisher information matrix (FIM) of the genericbursts of Figure 12 can be written as

F =

⎡⎢⎢⎣Fθθ Fθν FθαFνθ Fνν Fνα

Fαθ Fαν Fαα

⎤⎥⎥⎦

=

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

−Er{∣∣∣∣

a′′

∂θ2

∣∣∣∣}

−Er{∣∣∣∣

a′′

∂θ∂ν

∣∣∣∣}−Er

{∣∣∣∣a′′

∂θ∂α

∣∣∣∣}

−Er{∣∣∣∣

a′′

∂ν∂θ

∣∣∣∣}

−Er{∣∣∣∣

a′′

∂ν2

∣∣∣∣}

−Er{∣∣∣∣

a′′

∂ν∂α

∣∣∣∣}

−Er{∣∣∣∣

a′′

∂α∂θ

∣∣∣∣}−Er

{∣∣∣∣a′′

∂α∂ν

∣∣∣∣}

−Er{∣∣∣∣

a′′

∂α2

∣∣∣∣}

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

,

(B.1)

where a′′ = ∂2 ln p(r | α, ν, θ), p(r | α, ν, θ) is the probabilitydensity function of r = {r(k)}, with k ∈ K , conditioned on

(α, ν, θ). Now r(k) is a random Gaussian variable with vari-ance equal to σ2 = N0/(2Es) and mean equal to

s(k) = e j(θ+2πνkT+απk2T2) (B.2)

so that

p(r | α, ν, θ) =∏

k∈Kp(rk | α, ν, θ

)

= 1(2πσ2

)N exp

{− 1

2σ2

∑

k∈K

∣∣r(k)− s(k)∣∣2}.

(B.3)

As detailed in Appendix A, after taking the logarithm of(B.3), and after differentiating with respect to the unknownparameters, and calculating the expectation of the terms with


respect to r, we have

F = 1σ2

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

∑

k∈K(1) 2πT

∑

k∈Kk πT2

∑

k∈Kk2

2πT∑

k∈Kk 4π2T2

∑

k∈Kk2 2π2T3

∑

k∈Kk3

πT2∑

k∈Kk2 2π2T3

∑

k∈Kk3 π2T4

∑

k∈Kk4

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

, (B.4)

where, thanks to the symmetry of range K ,

∑

k∈Kk = 0,

∑

k∈Kk3 = 0. (B.5)

We finally get the expression of the FIM matrix as

F = 1σ2

⎡⎢⎢⎢⎢⎢⎢⎣

N 0 πT2∑

k∈Kk2

0 4π2T2∑

k∈Kk2 0

πT2∑

k∈Kk2 0 π2T4

∑

k∈Kk4

⎤⎥⎥⎥⎥⎥⎥⎦. (B.6)

With an even number of pilot fields (Figure 12(a)), we have

∑

k∈Kk2 = 2

xeven−1∑

n=0

N/2xeven∑

l=1

[(M/

(2xeven − 1

)− 1)

2

+ l +(

N

2xeven+

M

2xeven − 1

)n]2

,

∑

k∈Kk4 = 2

xeven−1∑

n=0

N/2xeven∑

l=1

[(M/

(2xeven − 1

)− 1)

2

+ l +(

N

2xeven+

M

2xeven − 1

)n]4

(B.7)

while, with an odd number of pilot fields (Figure 12(b)), weget

∑

k∈Kk2=2

N/(2xodd+1)−1∑

k=1

k2

+2xodd−1∑

n=0

N/(2xodd+1)∑

l=1

[(N/(2xodd + 1

)− 1)

2+l

+(

N

2xodd+

M

2xodd +1

)n+

M

2xodd

]2

,

∑

k∈Kk4=2

N/(2xodd+1)−1∑

k=1

k4

+2xodd−1∑

n=0

N/(2xodd+1)∑

l=1

[(N/(2xodd + 1

)− 1)

2+l

+(

N

2xodd+

M

2xodd +1

)n+

M

2xodd

]4

.

(B.8)

Note that, thanks to the symmetry of the burst, the el-ements Fθν, Fνθ , Fαν, Fνα are all zero, which means thatthe joint phase/Doppler-shift and Doppler-shift/Doppler-rate estimations are decoupled.

Calculating F−1, we obtain the VCRBs for the estimationof ν as follows:

F−1νν = VCRB(ν) = 1

2π2T2∑

k∈K k2

1Es/N0

, (B.9)

as the one found in (A.11) without any Doppler-rate. Theoptimal burst configuration that minimizes the VCRB for νis thus the 2P format found in [14] also in the presence ofDoppler-rate effects.

The VCRB for α is

F−1αα = VCRB(α) = − 2N

π2T4[(∑

k∈K k2)2−N

∑k∈K k4

] 1Es/N0

.

(B.10)

If we compute F−1αα as a function of x through (B.7) and

(B.8), for both configurations of Figure 12, we find that theminimum for F−1

αα is obtained with xodd = 1 in (B.8). Thiswas found by exhaustive numerical evaluation with practicalvalues for M and N. We can conclude that the VCRB of theerror variance of any unbiased estimator of α is always mini-mized for a configuration with three blocks of pilot symbolsequally spaced by two blocks of data symbols (3P format).Setting xodd = 1 in (B.8) and (B.10), the minimum VCRBof the error variance of any unbiased estimator of α for theoptimal 3P format is thus

VCRBmin(α)

= F−1αα

∣∣xodd=1 = VCRB3P(α)

= 9720 · (Es/N0)−1

/(π2T4N

[108

(4− 5N2 + N4)

+ 32MN(15N2 − 45

)

+ 24M2(35N2 − 45)

+ 720NM3 + 270M4]).(B.11)

In order to evaluate the gain in using the 3P for-mat, we have compared the VCRB3P(α) to the boundsfor α in other configurations. Figure 13 shows the ra-tios VCRB2P(α)/VCRB3P(α), VCRB4P(α)/VCRB3P(α), andVCRB2P(α)/VCRB4P(α) as functions of the total number Nof pilots and with η = 10%. It is clear that for practicalvalues of N = 40 ÷ 70, the 3P format exhibits a gain of10 log(78.6) = 19 dB in terms of Es/N0 with respect to the2P format and of 10 log(1.1) = 0.4 dB with respect to the 4Pformat. The accuracy of the 3P format and of the 4P formatcan be thus considered almost equivalent.


−40

−20

0

20

40

60

80

100

120

140

160

180

200

VC

RB

(α)

rati

os

0 10 20 30 40 50 60 70 80 90 100

N

VCRB2P (α)/VCRB3P (α)VCRB2P (α)/VCRB4P (α)VCRB4P (α)/VCRB3P (α)

78.671.9

1.09

Figure 13: VCRB2P(α)/VCRB3P(α), VCRB2P(α)/VCRB4P(α) andVCRB4P(α)/VCRB3P(α) ratios as function of the total number of pi-lots N .

The various VCRBs can be easily calculated from (B.10)using the appropriate x and (B.7) and (B.8). We report herethe final expressions

VCRB2P(α)

= F−1αα

∣∣xeven=1

= 360 · (Es/N0)−1

π2T4(N3 − 4N

)(4N2 + 15M2 + 15MN − 4

) ,

(B.12)

VCRB4P(α)

= F−1αα

∣∣xodd=2

=25920 · (Es/N0)−1

/(π2T4N

(288N4 + 1305N3M

+ 240NM(8M2 − 15

)

+ 30N2(77M2 − 48)

+ 32(20M4−75M2 + 36

))).

(B.13)

REFERENCES

[1] I. Ali, N. Al-Dhahir, and J. E. Hershey, “Doppler characteriza-tion for LEO satellites,” IEEE Transactions on Communications,vol. 46, no. 3, pp. 309–313, 1998.

[2] “Special Issue on communications in the intelligence trans-portation system,” IEEE Communications Magazine, vol. 34,1996.

[3] M. Morelli and U. Mengali, “Feedforward frequency estima-tion for PSK: a tutorial review,” European Transactions onTelecommunications, vol. 9, no. 2, pp. 103–116, 1998.

[4] F. Giannetti, M. Luise, and R. Reggiannini, “Simple carrier fre-quency rate-of-change estimators,” IEEE Transactions on Com-munications, vol. 47, no. 9, pp. 1310–1314, 1999.

[5] M. Morelli, “Doppler-rate estimation for burst digital trans-mission,” IEEE Transactions on Communications, vol. 50, no. 5,pp. 707–710, 2002.

[6] P. M. Baggenstoss and S. M. Kay, “On estimating the angle pa-rameters of an exponential signal at high SNR,” IEEE Transac-tions on Signal Processing, vol. 39, no. 5, pp. 1203–1205, 1991.

[7] T. J. Abatzoglou, “Fast maximum likelihood joint estima-tion of frequency and frequency rate,” IEEE Transactions onAerospace and Electronic Systems, vol. 22, no. 6, pp. 708–715,1986.

[8] T. S. Rappaport, Wireless Communications: Principles & Prac-tice, Prentice-Hall, Englewood Cliffs, NJ, USA, 1999.

[9] J. A. Gansman, J. V. Krogmeier, and M. P. Fitz, “Single fre-quency estimation with non-uniform sampling,” in Proceed-ings of the 30th Asilomar Conference on Signals, Systems andComputers, vol. 1, pp. 399–403, Pacific Grove, Calif, USA,November 1996.

[10] V. Lottici and M. Luise, “Embedding carrier phase recoveryinto iterative decoding of turbo-coded linear modulations,”IEEE Transactions on Communications, vol. 52, no. 4, pp. 661–669, 2004.

[11] S. Benedetto, R. Garello, G. Montorsi, et al., “MHOMS: high-speed ACM modem for satellite applications,” IEEE WirelessCommunications, vol. 12, no. 2, pp. 66–77, 2005.

[12] F. Rice, “Carrier-phase and frequency-estimation bounds fortransmissions with embedded reference symbols,” IEEE Trans-actions on Communications, vol. 54, no. 2, pp. 221–225, 2006.

[13] H. Minn and S. Xing, “An optimal training signal structure forfrequency-offset estimation,” IEEE Transactions on Communi-cations, vol. 53, no. 2, pp. 343–355, 2005.

[14] A. Adriaensen, A. Van Doninck, and W. Steinert, “MF-TDMAburst demodulatir design with pilot-symbol assisted frequencyestimation,” in Proceedings of the 8th International Workshopon Signal Processing for Space Communications (SPSC ’03),Catania, Italy, September 2003.

[15] L. Giugno and M. Luise, “Carrier frequency and frequencyrate-of-change estimators with preamble-postamble pilotsymbol distribution,” in Proceedings of IEEE International Con-ference on Communications (ICC ’05), vol. 4, pp. 2478–2482,Seoul, Korea, May 2005.

[16] A. Zhuang and M. Renfors, “Combined pilot aided and de-cision directed channel estimation for the RAKE receiver,” inProceedings of the 52nd IEEE Vehicular Technology Conference(VTC ’00), vol. 2, pp. 710–713, Boston, Mass, USA, September2000.

[17] U. Mengali and A. N. D’Andrea, Synchronization Techniquesfor Digital Receivers, Plenum Press, New York, NY, USA, 1997.

[18] F. Gini, R. Reggiannini, and U. Mengali, “The modifiedCramer-Rao bound in vector parameter estimation,” IEEETransactions on Communications, vol. 46, no. 1, pp. 52–60,1998.

[19] G. R. J. Povey and J. Talvitie, “Doppler compensation and codeacquisition techniques for LEO satellite mobile radio commu-nications,” in Proceedings of the 5th International Conference onSatellite Systems for Mobile Communications and Navigation,pp. 16–19, London, UK, May 1996.

[20] M. Luise and P. Reggiannini, “Carrier frequency recoveryin all-digital modems for burst-mode transmissions,” IEEETransactions on Communications, vol. 43, no. 2–4, pp. 1169–1178, 1995.

[21] D. C. Rife and R. R. Boorstyn, “Single-tone parameter estima-tion from discrete-time observations,” IEEE Transactions onInformation Theory, vol. 20, no. 5, pp. 591–598, 1974.


Research ArticleTCP-Call Admission Control Interaction inMultiplatform Space Architectures

Georgios Theodoridis,1 Cesare Roseti,2 Niovi Pavlidou,1 and Michele Luglio2

1 Department of Electrical & Computing Engineering, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece2 Dipartimento di Ingegneria Elettonica, Universita degli Studi di Roma Tor Vergata, Via del Politecnico 1, 00133 Rome, Italy

Received 28 September 2006; Revised 3 March 2007; Accepted 18 May 2007


The implementation of efficient call admission control (CAC) algorithms is useful to prevent congestion and guarantee target qual-ity of service (QoS). When TCP protocol is adopted, some inefficiencies can arise due to the peculiar evolution of the congestionwindow. The development of cross-layer techniques can greatly help to improve efficiency and flexibility for wireless networks.In this frame, the present paper addresses the introduction of TCP feedback into the CAC procedures in different nonterrestrialwireless architectures. CAC performance improvement is shown for different space-based architectures, including both satellitesand high altitude platform (HAP) systems.

Copyright © 2007 Georgios Theodoridis et al. This is an open access article distributed under the Creative Commons AttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properlycited.

1. INTRODUCTION

The development of network architectures including thespace segment (GEO satellites) aims to provide telecommu-nication services in wide geographical areas. The space seg-ment can complement or even replace the terrestrial infras-tructure wherever the latter either fails or is not cost effective.As a matter of fact, along with the evolution of new tech-nological solutions, such as high altitude platforms (HAPs)[1], next generation networks are envisioned as the integra-tion of several different subsystems, unconditionally interop-erating among one another [2]. Various architectures includ-ing combinations of GEO and HAPs are under continuousstudy so as to take advantage of each segment’s most favor-able features in terms of coverage area, easy and quick de-ployment, robustness to failure and to disaster occurrence,and so forth.

On the other hand, some of the protocols and techniquessupporting the communication through this heterogeneouswireless environment could be inadequate, since they arespecifically designed for wired networks. Nevertheless, theseprotocols and techniques are worth being utilized due totheir many desirable characteristics and to the fact that thewireless path is usually only a segment of the whole route be-tween the sender and the receiver.

One of these protocols is TCP [3, 4], which is the pre-dominant protocol at the transport layer when dealing with

the very popular Internet-based applications. It presents sev-eral impairments when it is implemented in wireless envi-ronments [5, 6]. In brief, TCP, originally designed to workwell over wired congested network, considers all losses asan explicit indication of network congestion [7]. Therefore,TCP control rate leads to unnecessary rate reductions andthen to severe performance degradation without taking intoaccount error-prone wireless links. Communication involv-ing long-delay segments (i.e., geostationary satellites), em-phasizes such an impairment slowing down the reversion tothe previous transmission rate.

In addition, the presence of asymmetric links may slowdown the acknowledgement flow causing problems in theforward channel as well, since TCP misinterprets the overallRTT increase as a congestion notification in the data direc-tion.

In parallel, CAC has evolved into one of the most signifi-cant bandwidth management tools in the case of both wiredand wireless networks. However, the efficiency of the CACprocess is highly dependent on the accuracy of the availableinfo concerning the transmission rate of the serviced connec-tions, not only at the time instant that the CAC algorithm isexecuted but also for the whole duration of these connec-tions. In particular, the CAC algorithm must be able to makea safe prediction regarding the availability of resources in thelong term in order to decide if a new connection can be ad-mitted into the system [8, 9].


In this frame, the present paper investigates the possibil-ity of introducing an interaction between TCP and CAC inseveral nonterrestrial wireless architectures, in order to im-prove CAC efficiency by taking TCP dynamics into account.More specifically, the exploitation of TCP feedback as inputfor the CAC algorithm at regular time intervals has provedto be of primary importance for maximizing the utilizationof the network resources [10]. However, as the TCP perfor-mance is rather dependent on the characteristics of the com-munication path, the implementation of the CAC-TCP inter-action on different system architectures will introduce mean-ingful improvements in all the architectures showing suchcharacteristics, demonstrating a more general importance ofthe concept. Additionally, so far, limited work can be foundin the literature on this topic.

The paper is organized as follows: Section 2 provides abrief analysis of the TCP driven CAC concept, while Section 3includes an overview of possible architectures. Section 4presents a description of the reference architectures and thesimulation scenario, along with results comparing the effi-ciency of the proposed algorithm in the several space archi-tectures. Finally, Section 5 summarizes the conclusions.

2. THE CONCEPT OF A TCP-BASED CAC

TCP is a transport layer protocol based on sending data pack-ets upon reception of acknowledgement of previously sentpackets, thus guaranteeing high reliability. When the net-work is characterized by significant round trip time (RTT),as in the case a satellite path is included, this process can sig-nificantly slow down data transfer.

TCP can exploit congestion control either through anACK counting mechanism (the actions on the sliding win-dow are just based on the number of received ACKs) [3] orthrough the byte-counting scheme (the actions on the slidingwindow are based on the actual number of bytes acknowl-edged) [11].

When the communication path is not error-free (usualin wireless networks) TCP misinterprets the data loss due tothe harsh wireless reception conditions as congestion occur-rence. As a consequence, for every packet loss, TCP reducesthe actual transmission rate, limiting the bandwidth utiliza-tion of the connection far below its nominal value.

This inefficiency is meaningful in wireless networks sincethe radio resource is usually scarce and expensive. Particu-larly in GEO satellite, the large footprints limit the imple-mentation of frequency reuse, thus reducing system capac-ity. Therefore, achieving maximum utilization of the avail-able bandwidth must be the primary goal of every networkconfiguration.

On the other hand, CAC is implemented by the networkmanager as a preventive congestion control scheme. CAC al-gorithms decide upon the admittance/rejection of new con-nections based on the network conditions (traffic load, linkcapacity, buffer size, etc.) as well as the traffic characteristicsand the QoS objectives of both the candidate and the alreadyactive users. In this framework, the aim of CAC is twofold: (i)to guarantee that the QoS requirements of all the admitted

users are met, and (ii) maximize revenue from the network’sperspective, that is, optimize the utilization of the availableresources [8]. However, achieving these objectives is ratherdifficult, since CAC is inherently an “in advance” procedureand no traffic model can offer a priori a completely accu-rate prediction, in particular considering the heterogeneityof multimedia telecommunication traffic sources. Therefore,real-time measurements of each connection’s load and con-ditions are considered essential for the CAC’s effectiveness[9].

CAC functionality is based on the concept that the usedbandwidth plus the bandwidth of the upcoming user shouldbe lower or equal to the total capacity. As a matter of fact thefollowing condition must be always respected:

N∑

i=1

Bi + Bf ≤ c. (1)

Since always Bj TCP datarate ≤ Bj nominal datarate, theexploitation of the TCP feedback leads to a decrease in thesystem overall blocking probability. Moreover, the band-width assigned to each connection is equal to the real datarate of the connection monitored via the TCP performance.Therefore, having maximized the average number of theusers simultaneously active in the network and having min-imized the over-assignment of resources, the throughput ofthe network, defined as the percentage of the aggregate ca-pacity that is actually occupied by the set of active connec-tions, is radically improved.

In this frame, the possibility to get feedback informa-tion about TCP congestion window actual evolution wouldbe of primary importance in order to efficiently drive CACscheme. In fact, since the CAC algorithm, by taking into ac-count the actual amount of capacity necessary to exploit allthe TCP connections, could prevent the over provision ofbandwidth to the aforementioned connections, a better uti-lization of the network resources would be achieved. In thisway, the admission/rejection of the new user would be basedon the actual occupancy of the channel by the active users atthe time instant of a new user arrival, computed according tothe TCP congestion window state of the connections insteadof their nominal data rate. The above scheme is depicted inthe flow chart of Figure 1.

3. SUITABLE ARCHITECTURES FORCAC-TCP INTERACTION

The potential improvement introduced by the implementa-tion of the integrated CAC-TCP scheme is addressed in var-ious nonterrestrial wireless architectures, where either thehigh propagation delay and/or the occurrence of transmis-sion errors negatively impact TCP performance by leading toan unjustified decrease of the transmission data rate.

In particular, four different architectures are introducedand described, focusing on the potential drawbacks concern-ing optimal TCP working.

Georgios Theodoridis et al. 3

Arrival of a new user Abelonging to the x QoS-class

and the y mobility group

The set of the N active users B = {Bj,}, j = 1, · · · ,N

TCP the transport protocolof the connection Bj

No

Yes

Bj real datarate = Bj TCP datarate;

BW occupied =N∑

j=1

Bj datarate;

A nominal datarate + BW occupied ≤ capacity

NoYes

A is blocked A is admitted

Bj real datarate = Bj nominal datarate;

Figure 1: Cross-layer CAC-TCP flow chart.

Core network

Figure 2: Stand-alone GEO satellite.

3.1. Stand-alone GEO satellite

A system architecture based on a stand alone GEO satellite(Figure 2) implies a rather challenging environment for TCPperformance. Such an architecture presents a long propaga-tion path (in average about 80 000 km end to end) along withtransmission errors quantified in terms of BER (depending onpropagation channel conditions) and link unavailability, par-

ticularly meaningful in case of use of high frequencies and/orterminal mobility.

The large latency-bandwidth product could cause twoharmful effects:

(i) the pipe size, indicating the amount on unacknowl-edged data that can be “in-flight” in a given instant,could exceed the buffer limits in the existing im-plementations resulting in a suboptimal maximumthroughput;

(ii) the high latency entails a considerable time interval toopen the TCP sliding window, when a new connectionstarts (slow-start algorithm). Similarly, in the case oflosses, the reaction of TCP is very slow, increasing thetime needed to return to high transmission rates.

3.2. Stand-alone HAP

HAPS are characterized by the utilization of a platform lo-cated in the stratosphere (about 20 km from ground), al-lowing very fast deployment, low cost, less critical commu-nication parameters, flexible architecture but limited cov-erage (Figure 3). The proximity of the HAP to the groundminimizes the propagation delay, being distances compa-rable to the ones in terrestrial wireless systems [1, 12].


Core network

Figure 3: Stand-alone HAP.

Nevertheless, since HAP systems work also in millimeter-wave bands (47/48 GHz), in that case rain attenuation andscattering constitute a severe constraint in achieving goodTCP performance. Some studies indicate a two-state (good-bad) Markov model as a suitable error model [13]. There-fore, the packet-error rate (PER) experienced by the TCP canbe approximated by the probability of the bad channel con-ditions.

Depending on the PER value, TCP congestion windowcontinuously stops its growth resulting in “fast retransmitand fast recovery” (FR-FR) or even timeout expirations,when due to the loss of a large burst of segments, sender doesnot receive any feedback (i.e., duplicate ACKs). In the lattercase, TCP remains in an idle state for several seconds and re-sets its window to one segment.

3.3. Integrated GEO satellite—HAP

In order to allow HAPS users to communicate with remotelocations, a link between the HAPS and the satellite can beenvisaged, as depicted in Figure 4.

Being the GEO-HAP segment outside the atmosphereand in line-of-sight (LoS) conditions, errors are due to freespace losses and thermal noise and quantified in terms ofBER. On the contrary, the PER of the overall link is predom-inately defined by the HAP-ground segment, where signifi-cant transmission errors can occur depending on the utilizedfrequency and on eventual ground terminal mobility. Thus,from the PER point of view an integrated GEO-HAP archi-tectures is equivalent to the stand-alone HAP case. Moreover,the use of GEO satellite as an intermediate node introduceslong RTT, adding the drawbacks in the TCP dynamics de-tected in the stand-alone GEO satellite scenario.

3.4. HAP constellation

Finally, we consider the architecture of Figure 5, where thecoverage area is served by a constellation of HAPs; inter-HAPlinks are also set up [14]. If the data is forwarded to the des-tination HAP via one (or more) of its neighboring HAPs, al-though the propagation delay is kept low, the end-to-end re-ception conditions could possibly become harsher, due to theimperfections of the inter-HAP links. The aforementionedimperfections could be mostly due to the stabilization prob-lems of the platforms, which would result in correspondingpointing difficulties regarding the optical links that are envi-sioned for such an inter-HAP communication.

Core network

Figure 4: Integrated GEO satellite—HAP.

Then, in this scenario, TCP performance suffers mainlyfrom the problems arisen in the stand-alone HAP architec-ture.

4. EVALUATION OF THE CAC-TCP INTERACTIONIN SPACE ARCHITECTURES

4.1. Reference architectures

Summarizing, TCP performance over radio links, includingone or more space systems, relies primarily on two factors:

(1) the delay imposed by the space segment (RTT),(2) the reception error probability of the wireless space-

user channel (PER).

The adopted TCP scheme, based on ACK counting, leads tosame efficiency as achievable when using the byte-countingalgorithm [11], because all the correctly delivered TCP pack-ets are considered immediately acknowledged by the corre-sponding ACK (ACK are not delayed).

Thus, in order to evaluate the efficiency as well as thenecessity of a TCP driven CAC scheme, only three differentnetwork architectures, based on the boundary conditions interms of RTT and PER (or both), are selected to be simulatedin the present paper. They are stand-alone GEO (Figure 2),stand-alone HAP (Figure 3), and integrated GEO satellite-HAP (Figure 4). In the following, the most meaningful im-plemented features concerning the selected architectures, aredescribed. In all the three architectures losses affect bothACK and TCP packet flows (ACK losses have a slight impacton the overall performance due to the cumulative nature ofACKs [4]).

Stand-alone GEO architecture

Data originating from the core network are forwarded via agateway toward the GEO satellite, which transparently redi-rects the stream (bent-pipe satellite) to the end users. Usersare considered to be fixed and equipped with VSATs appro-priately mounted so as to guarantee line-of-sight (LoS) con-dition for the satellite-user link. Therefore, since the signal-to-noise ratio (SNR) is not only maximized but also relativelyinvariant due to the absence of mobility, low PER value can


Core network

Figure 5: HAP constellation.

be assumed. Moreover, the gateway-satellite link is typicallydimensioned to be error free.

Stand-alone HAPS

In comparison with the previous architecture, the GEO satel-lite has been replaced with a HAP, while the data flow main-tains the same characteristics. The proximity of the HAP tothe earth greatly decreases link latency and facilitates the con-nectivity of mobile users. In more detail, in the GEO satellitescenario, a mobile terminal should be equipped with highpower transmission amplifier as well as sizeable antennas, soas to compensate the high free-space attenuation imposedby the long propagation path. These features lead to bulkyand power consuming (limited autonomy) terminals, com-pletely inappropriate for mobile use. On the contrary, pro-viding access via a HAP located at an altitude of 20 km al-lows the use of small, cost-efficient, and user-friendly de-vices. Consequently, the stand-alone HAPS scenario consid-ers mobile users, which are further divided into three cate-gories based on their mobility characteristics: highway-users,suburban-users, urban-users. In particular, highway-usersmove in open areas with maximum LoS probability, while, asthe city centre (suburban and urban users) is approached, thehigher building in combination with the narrow streets hin-der the LOS path and the received signal is the result of suc-cessive reflections (multipath). Moreover, according to thechannel model, even in the case of a highway user, the av-erage PER is much higher than in case of a fixed user that isserved by a GEO system.

Integrated GEO satellite—HAP

The rationale behind the integration of the two systems isthat one satellite can provide connectivity to multiple HAPsboth among each other and toward the core network, with-out the deployment of extra infrastructures. In this case, asdescribed in Section 3.4, the PER of the end-to-end link is de-termined by the PER of the user-HAP segment (equal to theof stand-alone HAP system), while the long RTT is imposedby the GEO-satellite segment (equal to the case of stand-alone GEO system).

As it becomes evident, the scenario involving a stand-alone GEO system with fixed users presents the highest RTTand the lowest PER, while the scenario involving a stand-alone HAP system presents the highest PER and the lowest

RTT. Finally, the integrated GEO-HAP scenario combinesthe characteristics of both of them, that is maximum RTTand maximum PER. Moreover, beyond the fact that thesenetwork scenarios present a wide range of RTT and PER val-ues, they are also the most significant in terms of servicesand applications. Therefore, the analysis of these case stud-ies can provide solid conclusions regarding the ability of theproposed TCP-CAC interaction to improve the network per-formance, in terms of both blocking probability and averagethroughput, in a great variety of channel conditions.

4.2. Simulation scenario and parameters

All the users are classified into three QoS classes accord-ing to the nominal rate of their connections: 128, 256, and512 kbps. The implementation of a weighted priority CACscheme, as the one proposed in [15], guarantees the provi-sion of equitable service of multiple parallel flows with dif-ferent bandwidth requirements. According to this admissioncontrol algorithm, the aggregate capacity of the system is di-vided into a number of segments equal to the number of QoSclasses. The width of each segment (i.e., the capacity percent-age assigned to each QoS class) is determined by manipulat-ing the desired blocking probability ratio between the QoSclasses. Thus, a new flow belonging to the QoSi class is ad-mitted to the network on the basis of the bandwidth commit-ted to the particular QoSi class. Instead, in the case of a CACscheme without any prioritization based on QoS class, theusers of the higher QoS classes would be practically excludedfrom the network, as it would be difficult to satisfy their ex-cessive bandwidth needs and they would be usually blockedin favor of users with lower data rate requirements. There-fore, a weighted priority CAC scheme as defined in [15] hasbeen taken as reference in our analysis presented hereafter.Furthermore, the TCP driven CAC scheme has been derivedfrom exactly the same notion, with the only difference that,as it has been described in Section 2, the TCP-CAC algorithmtakes into account the TCP feedback of the flows instead oftheir nominal data rate in the process of computing the uti-lization of the channel and the availability of resources.

Both the TCP driven and the reference CAC scheme, havebeen simulated through an offline combination of two sim-ulation tools that run sequentially. In particular, the networksimulator ns-2 [16] is used to configure the communica-tion scenario (nodes, link parameters, and communicationprotocols) and to obtain TCP statistics. Additionally, a C++


simulation tool gets as input the TCP statistics and providesthe following functionalities:

(i) it runs alternatively either the reference or the TCPdriven CAC scheme;

(ii) it calculates the instantaneous and the averagethroughput of the network;

(iii) it computes the connection blocking probability foreach QoS class as well as the connection blocking prob-ability of the network.

To reproduce a trustworthy network traffic, we have consid-ered packet error distribution (derived at TCP level) com-pliant to the HAP communication characteristics [13, 17],while satellite-HAP or satellite-user terminal link have beenconsidered as almost error free. The latter assumption israther realistic since satellite gateway EIRP can be set in or-der to counterbalance the atmosphere attenuation. Then, de-pending on the terminal mobility, the following PER distri-butions have been considered.

(i) Fixed and portable terminals have been assumed al-ways in line-of-sight (LoS) with the HAP/satellite.Thus, uniform packet loss distributions (TCP level)are considered with relatively low mean values (10−4

for fixed terminals and 10−3 for portable terminals).(ii) In case of mobile terminals, a two-state channel model

[13] is considered to feature the alternating LoS andshadowing conditions. Durations of “bad” and “good”states depend on the motion environment according tothe values reported in [17].

Furthermore, both arrival and termination of TCP connec-tions are managed by the C++ event driven simulator as Pois-son processes [15]. Thus, the time between two successivearrivals of users (τ) and the duration of each admitted con-nection (d) follow exponential distribution with mean value1/λ and 1/μ, respectively:

pdf(τ) = λ · e−λ·τ , E[τ] = 1λ

,

pdf(d) = μ · e−μ·d, E[d] = 1μ.

(2)

The parameters E[d] and E[τ] along with the aggregate num-ber of users in the network (S) determine the traffic load ofthe network (L).

4.3. Results

The impact of the TCP-CAC interaction on all the threeselected network configurations (GEO, HAPS, and GEO-HAPS) has been evaluated in terms of blocking probabilityand average throughput. Moreover, the blocking probabilityand the average throughput are calculated for both the basicand the TCP-based call admission control scheme.

Figure 6 presents the system blocking probability for dif-ferent traffic loads. Regardless the network architecture, thebasic-CAC algorithm leads in every case to the same block-ing probability for the whole variety of traffic loads, which is

0

10

20

30

40

50

60

70

Blo

ckin

gpr

obab

ility

(%)

7000 8000 9000 10000 11000 12000 13000

Average traffic load

GEO, TCP-CACGEO, basic-CACGEO-HAPS, TCP-CAC

GEO-HAPS, basic-CACHAPS, TCP-CACHAPS, basic-CAC

Figure 6: Blocking probability versus average traffic load.

expected, since only the nominal data rate of both the can-didate and the already admitted users is taken into accountduring the acceptance/rejection procedure. The fluctuationsin the TCP rate caused by the latency and the errors imposedby the different channels do not affect the admission proce-dure and therefore the curves regarding the basic-CAC al-gorithm for all the three scenarios completely coincide witheach other. On the contrary, TCP-CAC algorithms presentmuch lower blocking probability. Due to the TCP feedback,the system is able to calculate the actual occupancy of theavailable channels which is much lower than the one declaredby the users initially during their admittance. Therefore, theunused bandwidth is reassigned to new users that would oth-erwise be blocked.

Figure 7 presents the improvement (decrease) intro-duced to the system blocking probability by the TCP drivenCAC scheme in comparison to the basic-CAC scheme. Itallows the reader to compare the impact of the proposedscheme on architectures with different propagation charac-teristics. As it becomes apparent,

BP decreaseGEO < BP decreaseHAP < BP decreaseGEO-HAPS.(3)

This can be easily explained by the fact that in the case ofthe integrated GEO-HAPS system, the harsh reception en-vironment (long latency and high reception error probabil-ity) leads to a severe degradation of the TCP performanceand thus to an intense decrease in the actual data rate of theTCP connections. In fact, letting x be the aggregate amountof nominal traffic load applying for network resources and ythe amount of traffic actually forwarded through the networkchannels, simulations have demonstrated that

x > yGEO > yGEO-HAPS,

x > yHAP > yGEO-HAP.(4)


30

40

50

60

70

80

90

100

Dec

reas

ein

bloc

kin

gpr

obab

ility

(%)

7000 8000 9000 10000 11000 12000 13000

Average traffic load

GEOGEO-HAPSHAPS

Figure 7: Blocking probability decrease versus average traffic load.

This means that users of the GEO-HAPS network leave agreat percentage of the system resources unutilized and thus,in comparison with other architectures, the number of usersthat can be simultaneously served by a channel of given ca-pacity is much higher (lower blocking probability).

Moreover, results shown in Figure 7 lead us to the con-clusion that the exploitation of TCP-feedback is much morecrucial in a stand-alone HAP system (high PER, low RTT)than in a stand-alone GEO (high RTT, low PER) configura-tion. Then, an error prone communication path, even withlow RTT, can cause abrupt decrease in the connection trans-mission rate.

Blocking probability and average throughput are the twomain metrics of the network performance, each dealing withthe issue of the system efficiency from a different perspec-tive. Blocking probability must be minimized to maximizethe QoS (minimum delay) guaranteed to the users, while av-erage throughput must be maximized to maximize revenuesfor the network administrator. Figure 8 shows that there isalways a tradeoff between these two factors: increased aver-age throughput leads to increased blocking probability, whilelimitation of the blocking probability results in a low band-width utilization. In addition, from Figure 8 it is evident that,regardless of the network scenario, the implementation ofthe integrated TCP-CAC scheme results in the same averagethroughput for any given value of blocking probability. Thisis due to the fact that the admission control algorithm basesthe acceptance/rejection decision upon the knowledge of thereal traffic load forwarded at that given time through the net-work.

Therefore, a new connection is blocked only if there isno further available bandwidth. Thus, since the availabilityof resources occurs on the basis of the new connection nom-inal rate, for a given throughput, the blocking probability isthe same for all the possible scenarios (GEO, GEO-HAPS,HAPS). On the contrary, the basic-CAC algorithm assumes

30

40

50

60

70

80

90

100

Ave

rage

thro

ugh

put

(%)

0.1 1 10

Blocking probability (%)

GEO, TCP-CACGEO, basic-CACGEO-HAPS, TCP-CAC

GEO-HAPS, basic-CACHAPS, TCP-CACHAPS, basic-CAC

Figure 8: Average throughput versus blocking probability.

that the occupancy of the network capacity is equal to theaggregate of the nominal rates of all the active users. Conse-quently, the requests for new connections are rejected whilethere is still spare bandwidth. The average throughput for agiven blocking probability relies now upon the amount ofTCP data rate degradation. Therefore, the stand-alone GEOcase presents the higher average throughput and the inte-grated GEO-HAPS architecture the minimum one, as theypresent, respectively, the minimum and the maximum de-crease in the TCP data rate.

Finally, according to Figure 9 the lower the networkblocking probability is, the higher the gain from the utiliza-tion of the TCP feedback is. Moreover, the gain for the sce-narios with the worst reception conditions is higher, since thebasic-CAC algorithm severely limits the system throughput.

5. CONCLUSIONS AND FUTURE PERSPECTIVES

New and innovative wireless telecommunication architec-tures (including HAPs and satellite segments) are identifiedto provide broadband services in a cost-efficient and ubiqui-tous manner, ensuring seamless interoperation with the ex-isting infrastructure. To ensure network efficiency for sucharchitectures it is worth optimizing the performance of pro-tocols originally designed for terrestrial networks and forclassical architectures. Cross-layer techniques are becomingfundamental to cope with the dynamic variations character-izing wireless environments. The present paper focuses onoptimal utilization of the precious wireless resources whenflows running TCP share the channel. Referring to 5 differ-ent architectures based on HAP/satellite links, we have an-alyzed the potential drawbacks leading to suboptimal end-to-end performance. A TCP driven CAC scheme has beenproposed in order to guarantee QoS for multimedia ser-vices with different bandwidth requirements, guarantee an


30

40

50

60

70

80

90

100

110

Incr

ease

inav

erag

eth

rou

ghpu

t(%

)

0 10 20 30 40

Blocking probability (%)

GEOGEO-HAPSHAPS

Figure 9: Average throughput increase versus blocking probability.

optimal resource utilization, and reduce the system blockingprobability, without altering the TCP standard mechanisms.

Through simulation, we demonstrated a considerableimprovement on the performance with respect to a referenceCAC algorithm that takes into account only QoS require-ments and physical parameters.

ACKNOWLEDGMENT

This paper has been supported by the European IST-FP6project: “SatNEx II—Satellite Communications Network ofExcellence II.”

REFERENCES

[1] T. C. Tozer and D. Grace, “High-altitude platforms for wirelesscommunications,” Electronics and Communication EngineeringJournal, vol. 13, no. 3, pp. 127–137, 2001.

[2] S. Uskela, “Key concepts for evolution toward beyond 3G net-works,” IEEE Wireless Communications, vol. 10, no. 1, pp. 43–48, 2003.

[3] J. Postel, “Transmission Control Protocol,” IETF RFC 793,September 1981.

[4] W. Stevens, TCP/IP Illustrated. Volume 1: The Protocols,Addison-Wesley, Reading, Mass, USA, 1994.

[5] C. Partridge and T. J. Shepard, “TCP/IP performance oversatellite links,” IEEE Network, vol. 11, no. 5, pp. 44–49, 1997.

[6] P. Loreti, M. Luglio, R. Kapoor, et al., “Satellite systems per-formance with TCP-IP applications,” in Proceedings of IEEEMilitary Communications Conference on Communications forNetwork-Centric Operations: Creating the Information Force(MILCOM ’01), vol. 2, pp. 811–815, McLean, Va, USA, Oc-tober 2001.

[7] W. Stevens, “TCP Slow Start, Congestion Avoidance, Fast re-transmit, and Fast recovery Algorithms,” Internet RFC 2001,1997.

[8] H. G. Perros and K. M. Elsayed, “Call admission controlschemes: a review,” IEEE Communications Magazine, vol. 34,no. 11, pp. 82–91, 1996.

[9] K. Shiomoto, N. Yamanaka, and T. Takahashi, “Overview ofmeasurement-based connection admission control methodsin ATM networks,” IEEE Communications Surveys and Tuto-rials, vol. 2, no. 1, pp. 2–13, 1999.

[10] C. Roseti, G. Theodoridis, M. Luglio, and N. Pavlidou, “TCPdriven CAC scheme for HAPS and satellite integrated sce-nario,” in International Workshop on High Altitude PlatformSystems (WHAPS ’05), Athens, Greece, September 2005.

[11] M. Allman, “TCP Congestion Control with Appropriate ByteCounting (ABC),” RFC 3465, February 2003.

[12] S. Karapantazis and N. Pavlidou, “Broadband communica-tions via high-altitude platforms: a survey,” IEEE Communi-cations Surveys & Tutorials, vol. 7, no. 1, pp. 2–31, 2005.

[13] J. L. Cuevas-Ruız and J. A. Delgado-Penın, “Channel modelbased on semi-Markovian processes: an approach for HAPSsystems,” in Proceedings of the 14th International Conferenceon Electronics, Communications and Computers (CONIELE-COMP ’04), pp. 52–56, Veracruz, Mexico, February 2004.

[14] R. Miura and M. Oodo, “Wireless communications system us-ing stratospheric platforms: R & D program on telecom andbroadcasting system using high altitude platform stations,”Journal of the Communications Research Laboratory, vol. 48,no. 4, pp. 33–48, 2001.

[15] B. M. Epstein and M. Schwartz, “Predictive QoS-based admis-sion control for multiclass traffic in cellular wireless networks,”IEEE Journal on Selected Areas in Communications, vol. 18,no. 3, pp. 523–534, 2000.

[16] K. Fall and K. Varadhan, The ns manual, VINT Project, Uni-versity of California, Berkeley, Calif, USA, 2001, http://www.isi.edu/nsnam/ns/ns-documentation.html.

[17] Recommendation ITU-R P.681-6, “ITU-R P.681-6 Propaga-tion data required for the design of Earth-space land mobiletelecommunication systems,” January 2003.


Research ArticleEfficient Delay Tracking Methods with SidelobesCancellation for BOC-Modulated Signals

Adina Burian, Elena Simona Lohan, and Markku Kalevi Renfors

Institute of Communications Engineering, Tampere University of Technology, P.O. Box 553, 33101 Tampere, Finland

Received 26 September 2006; Accepted 2 July 2007


In positioning applications, where the line of sight (LOS) is needed with high accuracy, the accurate delay estimation is an im-portant task. The new satellite-based positioning systems, such as Galileo and modernized GPS, will use a new modulation type,that is, the binary offset carrier (BOC) modulation. This type of modulation creates multiple peaks (ambiguities) in the envelopeof the correlation function, and thus triggers new challenges in the delay-frequency acquisition and tracking stages. Moreover, theproperties of BOC-modulated signals are yet not well studied in the context of fading multipath channels. In this paper, sidelobecancellation techniques are applied with various tracking structures in order to remove or diminish the side peaks, while keep-ing a sharp and narrow main lobe, thus allowing a better tracking. Five sidelobe cancellation methods (SCM) are proposed andstudied: SCM with interference cancellation (IC), SCM with narrow correlator, SCM with high-resolution correlator (HRC), SCMwith differential correlation (DC), and SCM with threshold. Compared to other delay tracking methods, the proposed SCM ap-proaches have the advantage that they can be applied to any sine or cosine BOC-modulated signal. We analyze the performances ofvarious tracking techniques in the presence of fading multipath channels and we compare them with other methods existing in theliterature. The SCM approaches bring improvement also in scenarios with closely-spaced paths, which are the most problematicfrom the accurate positioning point of view.

Copyright © 2007 Adina Burian et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1. INTRODUCTION

Applications of new generations of Global Navigation Satel-lite Systems (GNSS) are developing rapidly and attract agreat interest. The modernized GPS proposals have been re-cently defined [1, 2] and the first version of Galileo (thenew European Satellite System) standards has been releasedin May 2006 [3]. Both GPS and Galileo signals use directsequence-code division multiple access (DS-CDMA) tech-nology, where code and frequency synchronizations are im-portant stages at the receiver. The GNSS receivers estimatejointly the code phase and the Doppler spreads through atwo-dimensional searching process in time-frequency plane.This delay-Doppler estimation process is done in two phases,first a coarse estimation stage (acquisition), followed by thefine estimation stage (tracking). The mobile wireless chan-nels suffer adverse effects during transmission, such as pres-ence of multipath propagation, high level of noise, or ob-struction of LOS by one or several closely spaced non-LOScomponents (especially in indoor environments). The fadingof channel paths induces a certain Doppler spread, related

to the terminal speed. Also, the satellite movement inducesa Doppler shift, which deteriorates the performance, if notcorrectly estimated and removed [4].

Since both the GPS and Galileo systems will send severalsignals on the same carriers, a new modulation type has beenselected. This binary offset carrier (BOC) modulation hasbeen proposed in [5], in order to get a more efficient shar-ing of the L-band spectrum by multiple civilian and militaryusers. The spectral efficiency is obtained by moving the signalenergy away from the band center, thus achieving a higherdegree of spectral separation between the BOC-modulatedsignals and other signals which use the shift-keying mod-ulation, such as the GPS C/A code. The BOC performancehas been studied for the GPS military M-signal [6] and laterhas been also selected for the use with the new Galileo sig-nals [3] and modernized GPS signals. The BOC modulationis a square-wave modulation scheme, which uses the typi-cal non-return-to-zero (NRZ) format [7]. While this type ofmodulation provides better resistance to multipath and nar-rowband interference [6], it triggers new challenges in the de-lay estimation process, since deep fades (ambiguities) appear


into the range of the ±1 chips around the maximum peakof the correlation envelope. Since the receiver can lock ona sidelobe peak, the tracking process has to cope with thesefalse lock points. In conclusion, the acquisition and track-ing processes should counteract all these effects, and differentmethods have been proposed in literature, in order to allevi-ate multipath propagation and/or side-peaks ambiguities.

In order to minimize the influence of multipath errors,which are the dominating error sources for many GNSS ap-plications, several receiver-internal correlation approacheshave been proposed. During the 1990’s, a variety of receiverarchitectures were introduced in order to mitigate the multi-path for GPS C/A code or GLONASS. The traditional GPS re-ceiver employs a delay-lock loop (DLL) with a spacing Δ be-tween the early and late correlators of one chip. However, dueto presence of multipath, this wide DLL, which should trackthe incoming signal within the receiver, is not able to alignperfectly the local code with the incoming signal, since thepresence of multipath (within a delay of 1.5 chips) creates abias of the zero-crossing point of the S-curve function. A firstapproach to reduce the influences of code multipath is thenarrow correlator or narrow early minus-late (NEML) track-ing loop introduced for GPS receivers by NovAtel [8]. Insteadof using a standard (wide) correlator, the chip spacing of anarrow correlator is less than one chip (typically Δ = 0.1chips). The lower bound on the correlator spacing dependson the available bandwidth. Correlator spacings of Δ = 0.1and Δ = 0.05 chips are commercially available for GPS.

Another family of tracking loops proposed for GPS arethe so-called double-delta (ΔΔ) correlators, which are thegeneral name for special code discriminators which areformed by two correlator pairs instead of one [9]. Somewell-known implementations of ΔΔ concept are the high-resolution correlator (HRC) [10], the Ashtech’s Strobe Cor-relator [11], or the NovAtel’s Pulse Aperture Correlator [12].Another similar tracking method with ΔΔ structure is theEarly1/Early2 tracking [13], where two correlators are lo-cated on the early slope of the correlation function (withan arbitrary spacing); their amplitudes are compared withthe amplitudes of an ideal reference correlation function andbased on the measured amplitudes and reference amplitudes,a delay correction factor is calculated. The Early1/Early2tracker shows the worst multipath performance for short-and medium-delay multipath compared to the HRC or theStrobe Correlator [9].

The early late slope technique [9], also called MultipathElimination Technology, is based on determining the slopeat both sides of autocorrelation function’s central peak. Onceboth slopes are known, they can be used to perform a pseu-dorange correction. Simulation results showed that in multi-path environments, the early late slope technique is outper-formed by HRC and Strobe correlators [9]. Also, it shouldbe mentioned that in cases of Narrow Correlator, ΔΔ, early-late slope, or Early1/Early2 methods the BOC(n,n) modu-lated signal outperforms the BPSK modulated signals, formultipath delays greater than approximately 0.5 chips (long-delay multipath) [9]. A scheme based on the slope differen-tial of the correlation function has been proposed in [14].

This scheme employs only the prompt correlator and in pres-ence of multipath, it has an unbiased tracking error, unlikethe narrow or strobe correlators schemes, which have a bi-ased tracking error due to the nonsymmetric property of thecorrelation output. However, the performance measure wassolely based on the multipath error envelope curves, thus itspotential in more realistic multipath environments is still anopen issue. One algorithm proposed to diminish the effectof multipath for GPS application is the multipath estimatingdelay locked loop (MEDLL) [15]. This method is different inthat it is not based on a discriminator function, but insteadforms estimates of delay and phase of direct LOS signal com-ponent and of the indirect multipath components. It usesa reference correlation function in order to determine thebest combinations of LOS and NLOS components (i.e., am-plitudes, delays, phases, and number of multipaths) whichwould have produced the measured correlation function.

As mentioned above, in the case of BOC-modulated sig-nals, besides the multipath propagation problem, the side-lobes peaks ambiguities should be also taken into account. Inorder to counteract this issue, different approaches have beenintroduced. One method considered in [16] is the partialSideband discriminator, which uses weighted combinationsof the upper and lower sidebands of received signal, to obtainmodified upper and lower signals. A “bump-jumping” algo-rithm is presented in [17]. The “bump-jumping” discrimi-nator tracks the ambiguous offset that arises due to multi-peaked Autocorrelation Function (ACF), making amplitudecomparisons of the prompt peak with those of neighbor-ing peaks, but it does not resolve continuously the ambigu-ity issue. An alternative method of preventing incorrect codetracking is proposed in [18]. This technique relies on sum-mation of two different discriminator S-curves (named hererestoring forces), derived from coherent, respectively non-coherent combining of the sidebands. One drawback is thatthere is a noise penalty which increases as carrier-to-noiseratio (CNR) decreases, but it does not seem excessive [18]. Anew approach which design a new replica code and producesa continuously unambiguous BOC correlation is describedin [19].

The methods proposed in [16–19] tend to destroy thesharp peak of the ACF, while removing its ambiguities. How-ever, for accurate delay tracking, preserving a sharp peak ofthe ACF is a prerequisite. An innovative unambiguous track-ing technique, that keeps the sharp correlation of the mainpeak, is proposed in [20]. This approach uses two correlationchannels, completely removing the side peaks from the corre-lation function. However, this method is verified for the par-ticular case of SinBOC(n,n) modulated signals, and its ex-tension to other sine or cosine BOC signals is not straightfor-ward. A similar method, with a better multipath resistance, isintroduced in [21].

Another approach which produces a decrease of sidelobesfrom ACF is the differential correlation method, where thecorrelation is performed between two consecutive outputs ofcoherent integration [22].

In this paper, we analyze in details and develop further anovel class of tracking algorithms, introduced by authors in

Adina Burian et al. 3

[23]. These techniques are named the sidelobes cancellationmethods (SCM), because they are all based on the idea ofsuppressing the undesired lobes of the BOC correlation en-velope and they cope better with the false lock points (ambi-guities) which appear due to BOC modulation, while keepingthe sharp shape of the main peak. It can be applied in bothacquisition and tracking stages, but due to narrow width ofthe main peak, only the tracking stage is considered here.In contrast with the approach from [20] (valid only for sineBOC(n,n) cases), our methods have the advantage that theycan be generalized to any sine and cosine BOC(m,n) modu-lation and that they have reduced complexity, since they arebased on an ideal reference correlation function, stored at re-ceiver side. In order to deal with both sidelobes ambiguitiesand multipath problems, we used the sidelobes cancellationidea in conjunction with different discriminators, based onthe unambiguous shape of ACF (i.e., the narrow correlator,the high resolution correlator), or after applying the differ-ential correlation method. We also introduced here an SCMmethod with multipath interference cancellation (SCM IC),where the SCM is used in combination with a MEDLL unit,and also an SCM algorithm based on threshold comparison.

This paper is organized as follows: Section 2 describes thesignal model in the presence of BOC modulation. Section 3presents several representative delay tracking algorithms,employed for comparison with the SCM methods. Section 4introduces the SCM ideas and presents the SCM usage inconjunction with other delay tracking algorithms or basedsolely on threshold comparison. The performance evalua-tion of the new methods with the existing delay estimators,in terms of root mean square error (RMSE) and mean timeto lose lock (MTLL), is done in Section 5. The conclusionsare drawn in Section 6.

2. SIGNAL MODEL IN PRESENCE OFBOC MODULATION

At the transmitter, the data sequence is first spread and thepseudorandom (PRN) sequence is further BOC-modulated.The BOC modulation is a square subcarrier modulation,where the PRN signal is multiplied by a rectangular sub-carrier which has a frequency multiple of code frequency. ABOC-modulated signal (sine or cosine) creates a split spec-trum with the two main lobes shifted symmetrically from thecarrier frequency by a value of the subcarrier frequency fsc

[5].The usual notation for BOC modulation is BOC( fsc, fc),

where fc is the chip frequency. For Galileo signals, theBOC(m,n) notation is also used [5], where the sine and co-sine BOC modulations are defined via two parametersm andn, satisfying the relationships m = fsc/ fref and n = fc/ fref,where fref = 1.023 MHz is the reference frequency [5, 24].From the point of view of equivalent baseband signal, BOCmodulation can be defined via a single parameter, denotedby the BOC-modulation order NBOC1 = 2m/n = 2 fsc/ fc. Thefactor NBOC1 is an integer number [25].

Examples of sine BOC-modulated waveforms for Sin-BOC(1, 1) (even BOC-modulation order NBOC1 = 2) and

1

0

−10 1 2 3 4 5

PRN sequence (NBOC1 = 1)

BO

C-m

odu

late

dco

de

Chips

1

0

−10 1 2 3 4 5

NBOC1 = 2

BO

C-m

odu

late

dco

de

Chips

1

0

−10 1 2 3 4 5

NBOC1 = 3

BO

C-m

odu

late

dco

deChips

Figure 1: Examples of time-domain waveforms for sine BOC-modulated signals.

SinBOC(15, 10) (odd BOC-modulation order NBOC1 = 3)together with the original PRN sequence (NBOC1 = 1) areshown in Figure 1. In order to consider the cosine BOC-modulation case, a second BOC-modulation order NBOC2 =2 has been defined in [25], in a way that the case of sine BOC-modulation corresponds to NBOC2 = 1 and the case of cosineBOC modulation corresponds to NBOC2 = 2 (see the expres-sions of (1) to (4)). After spreading and BOC modulation,the data sequence is oversampled with an oversampled factorofNs, and this oversampling determines the desired accuracyin the delay estimation process. Thus, the oversampling fac-tor Ns represents the number of samples per BOC interval,and one chip will consists of NBOC1NBOC2Ns samples (i.e, thechip period is Tc = NsNBOC1NBOC2Ts, where Ts is the sam-pling rate).

The BOC-modulated signal sn,BOC(t) can be written, inits most general form, as a convolution between a PRN se-quence sPRN(t) and a BOC waveform sBOC(t) [25]:

sn,BOC(t)

=+∞∑

n=−∞bn

SF∑

k=1

(−1)nNBOC1 ck,nsBOC(t − nT − kTc

)

= sBOC(t)⊗+∞∑

n=−∞

SF∑

k=1

bnck,n(−1)nNBOC1 δ(t − nT − kTc

)

= sBOC(t)⊗ sPRN(t),(1)


where bn is the nth complex data symbol, T is the symbolperiod (or code epoch length) (T = SFTc), ck,n is the kthchip corresponding to the nth symbol, Tc = 1/ fc is the chipperiod, SF is the spreading factor (i.e., for GPS C/A signaland Galileo OS signal, SF = 1023), δ(t) is the Dirac pulse,⊗ is the convolution operator and sPRN(t) is the pseudo-random (PRN) code sequence (including data modulation)of satellite of interest, and sBOC(·) is the BOC-modulatedsignal (sine or cosine) whose expression is given in (2) to(4). We remark that the term (−1)nNBOC1 is included to takeinto account also odd BOC-modulation orders, similar with[26]. The interference of other satellites is modeled as addi-tive white Gaussian noise, and, for clarity of notations, thecontinuous-time model is employed here. However, the ex-tension to the discrete-time model is straightforward and allpresented results are based on discrete-time implementation.

The SinBOC-CosBOC-modulated waveforms sBOC(t) aredefined as in [5, 25]:

ssin /CosBOC(t) =

⎧⎪⎪⎪⎨⎪⎪⎪⎩

sign(

sin(NBOC1πt

Tc

))for SinBOC,

sign(

cos(NBOC1πt

Tc

))for CosBOC,

(2)

respectively, that is, for SinBOC-modulation [25],

sSinBOC(t) =NBOC1−1∑

i=0

(−1)i pTB1

(t − i Tc

NBOC

), (3)

and for CosBOC-modulation [25],

sCosBOC(t) =NBOC1−1∑

i=0

NBOC2−1∑

k=0

(−1)i+k

× pTB

(t − i Tc

NBOC1

− k TcNBOC1NBOC2

).

(4)

In (3) and (4), pTB1(·) is a rectangular pulse of sup-

port Tc/NBOC1 and pTB (·) is a rectangular pulse of supportTc/NBOC1NBOC2 . For example,

pTB (t) =

⎧⎪⎨⎪⎩

1 if 0 ≤ t <Tc

NBOC1NBOC2

,

0 otherwise.(5)

We remark that the bandlimiting case can also be taken intoaccount, by setting pTB (·) to be equal to the pulse shapingfilter.

Some examples of the normalized power spectral den-sity (PSD), computed as in [25], for several sine and cosineBOC-modulated signals, are shown in Figure 2. It can be ob-served that for even-modulation orders such as SinBOC(1, 1)or CosBOC(10, 5) (currently selected or proposed by GalileoSignal Task Force), the spectrum is symmetrically split intotwo parts, thus moving the signal energy away from DC fre-quency and thus allowing for less interference with the exist-ing GPS bands (i.e., the BPSK case). Also, it should be men-tioned that in case of an odd BOC-modulation order (i.e.,

−2 −1 0 1 2

−120

−100

−80

−60

−40

−20

0

Frequency (MHz)

BPSKSinBOC (1, 1)

SinBOC (15, 10)CosBOC (10, 5)

Examples of PSD for different BOC-modulated signals

PSD

(dB

/Hz)

Figure 2: Examples of baseband PSD for BOC-modulated signals.

SinBOC(15, 10)), the interference around the DC frequencyis not completely suppressed.

The baseband model of the received signal r(t) via a fad-ing channel can be written as [25]

r(t) =√Ebe

+ j2π fDtn=+∞∑

n=−∞bn

L∑

l=1

αn,l(t)

× sn,sin /CosBOC(t − τl

)+ η(t),

(6)

where Eb is the bit or symbol energy of signal (one symbol isequivalent with a code epoch and typically has a duration ofT = 1 ms), fD is the Doppler shift introduced by channel, Lis the number of channel paths, αn,l is the time-varying com-plex fading coefficient of the lth path during the nth codeepoch, τl is the corresponding path delay (assuming to beconstant or slowly varying during the observation interval)and η(·) is the additive noise component which incorporatesthe additive white noise from the channel and the interfer-ence due to other satellites.

At the receiver, the code-Doppler acquisition and track-ing of the received signal (i.e., estimating the Doppler shift fDand the channel delay τl) are based on the correlation with a

reference signal sref(t−τ, fD,n1), including the PRN code andthe BOC modulation (here, n1 is the considered symbol in-dex):

sref(t − τ, fD,n1

)

= e− j2π fDtSF∑

k=−1

ck,n1

NBOC1−1∑

i=0

NBOC2−1∑

j=0

(−1)i+ j pTB

(t − n1T − kTc − i Tc

NBOC1

− jTc

NBOC1NBOC2

− τ).

(7)

Some examples of the absolute value of the ideal ACF forseveral BOC-modulated PRN sequences, together with the


BPSK case, are illustrated in Figure 3. As it can be observed,for any BOC-modulated signal, there are ambiguities withinthe ±1 chips interval around the maximum peak.

After correlation, the signal is coherently averaged overNc ms, with the maximum coherence integration length dic-tated by the coherence time of the channel, by possible resid-ual Doppler shift errors and by the stability of oscillators. Ifthe coherent integration time is higher than the coherencetime of the channel, the spectrum of the received signal willbe severely distorted. The Doppler shift due to satellite move-ment is estimated and removed before performing the coher-ent integration. For further noise reduction, the signal can benoncoherently averaged over Nnc blocks; however there aresome squaring losses in the signal power due to noncoher-ent averaging. The delay estimation is performed on a code-Doppler search space, whose values are averaged correlationfunctions with different time and frequency lags, with max-ima occurring at f = fD and τ = τl.

3. EXISTING DELAY ESTIMATION ALGORITHMS INMULTIPATH CHANNELS

The presence of multipath is an important source of errorfor GPS and Galileo applications. As mentioned before, tra-ditionally, the multipath delay estimation block is imple-mented via a feedback loop. These tracking loop methods arebased on the assumption that a coarse delay estimate is avail-able at receiver, as result of the acquisition stage. The trackingloop is refining this estimate by keeping the track of the pre-vious estimate.

3.1. Narrow early minus late (NEML) correlator

One of the first approaches to reduce the influences of codemultipath is the narrow early minus late correlation method,first proposed in 1992 for GPS receivers [8]. Instead of us-ing a standard correlator with an early late spacing Δ of 1chip, a smaller spacing (typically Δ = 0.1 chips) is used.Two correlations are performed between the incoming sig-nal r(t) and a late (resp., early) version of the reference codesrefEarly,Late (t − τ ± Δ/2), where srefEarly,Late (·) is the advanced ordelayed BOC-modulated PRN code and τ is the tentativedelay estimate. The early (resp., late) branch correlationsRearly,Late(·) can be written as

REarly,Late(τ) =∫

Nc

r(t)srefEarly,Late

(t − τ ± Δ

2

)dt. (8)

These two correlators spaced at Δ (e.g., Δ = 0.1 chips) areused in the receiver in order to form the discriminator func-tion. If channel and data estimates are available, the NEMLloops are coherent. Typically, due to low CNR and residualDoppler errors from GPS and Galileo systems, noncoherentNEML loops are employed, when squaring or absolute valueare used in order to compensate for data modulation andchannel variations. The performance of NEML is best illus-trated by the S-curve, which presents the expected value oferror as a function of code phase error. For NEML, the two

1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0−1.5 −1 −0.5 0 0.5 1 1.5

Nor

mal

ized

AC

Fs

Chips

Ideal ACF for BOC-modulated signals

BPSKSinBOC (1, 1)

SinBOC (15, 10)CosBOC (10, 5)

Figure 3: Examples of absolute value of the ACF for BOC-modulated signals.

branches are combined noncoherently, and the S-curve is ob-tained as in (9),

SNEML(τ) = ∣∣RLate(τ)∣∣2 − |REarly(τ)

∣∣2. (9)

The error signal given by the S-curve is fed back intoa loop filter and then into a numeric controlled oscilla-tor (NCO) which advances or delays the timing of the ref-erence signal generator. Figure 4 illustrates the S-curve insingle path channel, for BPSK, SinBOC(1, 1), respectively,SinBOC(10, 5) modulated signals. The zerocrossing showsthe presence of channel path, that is, the zero delay er-ror corresponds to zero feedback error. However, for BOC-modulated signals, due to sidelobes ambiguities, the early latespacing should be less than the width of the main lobe ofthe ACF envelope, in order to avoid the false locks. Typically,for BOC(m,n) modulation, this translates to approximatelyΔ ≤ n/4m.

3.2. High-resolution correlator (HRC)

The high-resolution correlator (HRC), introduced in [10],can be obtained using multiple correlator outputs from con-ventional receiver hardware. There are a variety of combi-nations of multiple correlators which can be used to imple-ment the HRC concept, which yield similar performance.The HRC provides significant code multipath mitigation formedium and long delay multipath, compared to the con-ventional NEML detector, with minor or negligible degrada-tion in noise performance. It also provides substantial carrierphase multipath mitigation, at the cost of significantly de-graded noise performance, but, it does not provide rejectionof short delay multipath [10]. The block diagram of a non-coherent HRC is shown in Figure 5. In contrast to the NEMLstructure, two new branches are introduced, namely, a very


1

0.8

0.6

0.4

0.2

0

−0.2

−0.4

−0.6

−0.8

−1−1.5 −1 −0.5 0 0.5 1 1.5

Nor

mal

ized

S-cu

rve

Delay error (chips)

Ideal S-curve (no multipath) forBOC-modulated and BPSK signals

BPSK

SinBOC (1, 1)SinBOC (10, 5)

Figure 4: Ideal S-curves for BOC-modulated and BPSK signals(NEML, Δ = 0.1 chips).

I & D onNc msec

I & D onNc msec

I & D onNc msec

I & D onNc msec

Late code

Early code

Very early code

Very late code

Constant factor a

NCO Loop filter

r(t)

+

− +

+

+

−

| |2

| |2

| |2

| |2

Figure 5: Block diagram for HRC tracking loop.

early and, respectively, a very late branch. The S-curve for anoncoherent five-correlator HRC can be written as in [10]:

SHRC(τ) = ∣∣RLate(τ)∣∣2 − ∣∣REarly(τ)

∣∣2

+ a(∣∣RVeryLate(τ)

∣∣2 − ∣∣RVeryEarly(τ)∣∣2)

,(10)

where RVeryLate(·) and RVeryEarly(·) are the very late and veryearly correlations, with the spacing between them of 2Δchips, and a is a weighting factor which is typically−1/2 [10].

Examples of S-curves for HRC in the presence of a sin-gle path static channel, are shown in Figure 6, for two BOC-modulated signals. The early late spacing is Δ = 0.1 chips(i.e., narrow correlator), thus the main lobes around zerocrossing are narrower, and it is more likely that the separa-tion between multiple paths will be done more easily.

1

0.8

0.6

0.4

0.2

0

−0.2

−0.4

−0.6

−0.8

−1−1.5 −1 −0.5 0 0.5 1 1.5

Nor

mal

ized

S-cu

rve

Delay error (chips)

Ideal S-curve (no multipath) for two BOC-modulated signals


Figure 6: Ideal S-curves for noncoherent HRC with a = −1/2, fortwo BOC-modulated signals and Δ = 0.1 chips.

3.3. Multipath estimating delay locked loop (MEDLL)

A different approach, proposed to remove the multipath ef-fects for GPS C/A delay tracking is the multipath estima-tion delay locked l;oop [15]. The MEDLL method estimatesjointly the delays, phases, and amplitudes of all multipaths,canceling the multipath interference. Since it is not based onan S-curve, it can work in both feedback and feedforwardconfigurations. To the authors’ knowledge, the performanceof MEDLL algorithm for BOC modulated signals is still notwell understood, therefore, would be interesting to study asimilar approach. The steps of the MEDLL algorithm (as im-plemented by us) are summarized bellow.

(i) Calculate the correlation function Rn(t) for the nthtransmitted code epoch. Find out the maximum peakof the correlation function and the corresponding de-

lay τ1, amplitude a1,n, and phase θ1,n.(ii) Subtract the contribution of the calculated peak, in or-

der to have a new approximation of the correlation

function R(1)n (τ) = Rn(τ)− a1,nRref(t − τ1,n)e jθ1,n . Here

Rref(·) is the reference correlation function, in the ab-sence of multipaths (which can be, for example, storedat the receiver). Find out the new peak of the residualfunction R(1)

n (·) and its corresponding delay τ2,n, am-

plitude a2,n, and phase θ2,n. Subtract the contributionof the new peak of residual function from R(1)

n (t) andfind a new estimate of the first peak. For more thantwo peaks, the procedure is continued until all desiredpeaks are estimated.

(iii) The previous step is repeated until a certain criterionof convergence is met, that is, when residual functionis below a threshold (e.g., set to 0.5 here) or until


1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0−1.5 −1 −0.5 0 0.5 1 1.5

Nor

mal

ized

AC

F

Delay error (chips)

Ideal ACFs (no multipath) for SinBOC (1, 1)-modulated signal

Non-coherent integrationDifferential correlation

Figure 7: Envelope correlation function of traditional noncoher-ent integration and differential correlation for a SinBOC(1, 1)-modulated signal.

the moment when introducing a new delay does notimprove the performance in the sense of root meansquare error between the original correlation functionand the estimated correlation function.

3.4. Differential correlation (DC)

Originally proposed for CDMA-based wireless communi-cation systems, the differential correlation method has alsobeen investigated in context of GPS navigation system [22]. Ithas been observed that with low and medium coherent timesof the fading channel and in absence of any frequency error,this approach provides better resistance to noise than the tra-ditional noncoherent integration methods. In DC method,the correlation is performed between two consecutive out-puts of coherent integration. These correlation variables arethen integrated, in order to obtain a differential variable. Thedifferential detection variable z is given as

zDC = 1M − 1

M−1∑

k=1

∣∣y∗k yk+1∣∣2

, (11)

where yk, k = 1, . . . ,M are the outputs of the coherent in-tegration and M is the differential integration length. For afair comparison between the differential noncoherent andtraditional noncoherent methods, here it is assumed thatM = Nnc, where Nnc is the noncoherent integration length.Since the differential coherent correlation method was no-ticed to be more sensitive to residual Doppler errors, onlythe differential noncoherent correlation is considered here.

The analysis done in [22] is limited to BPSK modulation.From Figure 7, it can be noticed that applying the DC to aBOC-modulated signal, instead of the conventional nonco-herent integration, the sidelobes envelope can be decreased,

and thus this method has a potential in reducing the sidepeaks ambiguities.

3.5. Nonambiguous BOC(n,n) signal tracking(Julien&al. method)

A recent tracking approach, which removes the sidelobesambiguities of SinBOC(n,n) signals and offers an improvedresistance to long-delay multipath, has been introduced in[20]. This method, referred here as Julien&al. method, af-ter the name of the first author in [20], has emerged whileobserving the ACF of a SinBOC(1, 1) signal with sine phas-ing, and the cross correlation of SinBOC(1, 1) signal with itsspreading sequence. The ideal correlation function Rideal

BOC(·)for SinBOC(1, 1)-modulated signals in the absence of multi-paths, can be written as [25]

RidealBOC(τ) = ΛTc/2(τ)− 1

2ΛTc/2

(τ − Tc

2

)− 1

2ΛTc/2

(τ +

Tc2

),

(12)

where ΛTc/2(τ − α) is the value in τ of a triangular function1

centered in α, with a width of 1-chip, Tc is the chip period,and τ is the code delay in chips.

The cross correlation of a SinBOC(1, 1) signal with thespreading pseudorandom code, for an ideal case (no multi-paths and ideal PRN code), can be expressed as [20]

RidealBOC,PRN(τ) = 1

2

(ΛTc/2

(τ +

Tc2

)+ΛTc/2

(τ − Tc

2

)).

(13)

Two types of DLL discriminators have been consideredin [20], namely, the early-minus- late- power (EMLP) dis-criminator and the dot-product (DP) discriminator. Theseexamples of possible discriminators result from the use ofthe combination of BOC-autocorrelation function and ofthe BOC/PRN-correlation function [20]. Based on (12) and(13), the ideal EMLP discriminator is constructed, as in (14),where τ is the code tracking error [20]:

SidealEMLP(τ) =

[Rideal2

BOC

(τ +

Δ

2

)− Rideal2

BOC

(τ − Δ

2

)]

−[Rideal2

BOC,PRN

(τ +

Δ

2

)− Rideal2

BOC,PRN

(τ − Δ

2

)].

(14)

The alternative DP discriminator variant [20] does nothave a linear variation as a function of code tracking error:

SidealDP (τ)

=[Rideal2

BOC

(τ +

Δ

2

)− Rideal2

BOC

(τ − Δ

2

)]Rideal2

BOC (τ)

−[Rideal2

BOC,PRN

(τ +

Δ

2

)− Rideal2

BOC,PRN

(τ − Δ

2

)]Rideal2

BOC (τ).

(15)

1 Our notation is equivalent with the notation triα(x/y) used in [20], viatriα(τ/y) = ΛTc/2(τ − αTc/y).


1

0.5

0−1.5 −1 −0.5 0 0.5 1 1.5

SinBOC (1, 1) modulation, ACFs ofBOC-modulated and subtracted signals

Continue line:BOC-modulated signal

Dashed line:subtracted signal

Delay (chips)

1

0.5

0

−1.5 −1 −0.5 0 0.5 1 1.5

SinBOC (1, 1) modulation, ACF of unambiguous signal

Unambiguous signal

Delay (chips)

Figure 8: SinBOC(1, 1)-modulated signal: examples of the ambigu-ous correlation function and subtracted pulse (upper plot) andthe obtained unambiguous correlation function (lower plot), for asingle-path channel.

Since the resulting discriminators remove the effect ofSinBOC(1, 1) modulation, there are no longer false lockpoints, and the narrow structure of the main correlation lobeis preserved [20]. Indeed, the side peaks of SinBOC(1, 1)correlation function Rideal

BOC(τ) have the same magnitudeand same location as the two peaks of SinBOC(1, 1)/PRN-correlation function Rideal

BOC,PRN(τ). By subtracting the squaresof the two functions, a new synthesized correlation functionis derived and the two side peaks of SinBOC(1, 1) correlationfunction are canceled almost totally, while still keeping thesharpness of the main lobe (Figure 8). Two small negativesidelobes appear next to the main peak (about ±0.35 chipsaround the global maximum), but since they point down-wards, they do not bring any threat [20]. The correlation val-ues spaced at more than 0.5 chips apart from the global peakare very close to zero, which means a potentially strong resis-tance to long-delay multipath.

In practice, the discriminators SEMLP(τ) or SDP(τ), asgiven in [20], are formed via continuous computation, at re-ceiver side, of correlation functions RBOC(·) and RBOC,PRN(·)values, not on the ideal ones. In practice, RBOC(·) is thecorrelation between the incoming signal (in the presence ofmultipaths) and the reference BOC-modulated code, andRBOC,PRN(·) is the correlation between the incoming signaland the pseudorandom code (without BOC modulation).This method has been applied only to SinBOC(n,n) signals.Moreover, instead of making use of the ideal reference func-tion Rideal

BOC,PRN(·) (which can be computed only once andstored at the receiver side), the correlation RBOC,PRN(·) needsto be computed for each code epoch in [20]. Of course, in or-der to make use of the Rideal

BOC,PRN(·) shape, we also need someinformation about channel multipath profile. This will be ex-plained in the next section.

4. SIDELOBES CANCELLATION METHOD (SCM)

In this section, we introduce unambiguous tracking ap-proaches based on sidelobe cancellation; all these approachesare grouped under the generic name of sidelobes cancel-lation methods). The SCM technique removes or dimin-ishes the threats brought by the sidelobes peaks of theBOC-modulated signals. In contrast with the Julien&al.method, which is restricted to the SinBOC(n,n) case, wewill show here how to use SCM with any sine or cosineBOC-modulated signal. The SCM approach uses an idealreference correlation function at receiver, which resemblesthe shapes of sidelobes, induced by BOC modulation. Inorder to remove the sidelobes ambiguities, this ideal refer-ence function is subtracted from the correlation of the re-ceived BOC-modulated signal with the reference PRN code.In the Julien&al. method, the subtraction function, whichapproximates the sidelobes, is provided by cross-correlatingthe spreading PRN code and the received signal. Here, thissubtraction function is derived theoretically, and computedonly once per BOC signal. Then, it is stored at the receiverside in order to reduce the number of correlation operations.Therefore, our methods provide a less time-consuming andsimpler approach, since the reference ideal correlation func-tion is generated only once and can be stored at receiver.

4.1. Ideal reference functions for SCM method

In this subsection, we explain how the subtraction pulsesare computed and then applied to cancel the undesired side-lobes.

Following derivations similar with those from [25] andintuitive deductions, we have derived the following ideal ref-erence function to be subtracted from the received signal af-ter the code correlation:

Ridealsub (τ) =

NBOC1−1∑

i=0

NBOC1−1∑

j=0

NBOC2−1∑

k=0

NBOC2−1∑

l=0

(−1)i× j+k+lΛTB

(τ + (i− j)TB + (k − l) TB

NBOC2

),

(16)

where TB = Tc/NBOC1NBOC2 is the BOC interval, ΛTB (·)is the triangular function centered at 0 and with a widthof 2TB-chips, NBOC1 is the sine BOC-modulation order(e.g., NBOC1 = 2 for SinBOC(1, 1), or NBOC1 = 4for SinBOC(10, 5)) [25], and NBOC2 is the second BOC-modulation factor which covers sine and cosine cases, as ex-plained in [25] (i.e., if sine BOC modulation is employed,NBOC2 = 1 and, if cosine BOC modulation is employed,NBOC2 = 2).

As an example, the simplest case of SinBOC(1, 1)-modulation (i.e., the main choice for Open Services inGalileo), (16) becomes

Ridealsub,SinBOC(1,1)(τ) = (ΛTB

(τ − TB

)+ΛTB

(τ + TB

)), (17)


which is similar with Julien& al. expression of (13) with theexception of a 1/2 factor (here, TB = Tc/2).

The Sin- and CosBOC(m,n)-based ideal autocorrelationfunction can be written as [25]

RidealBOC(τ) =

NBOC1−1∑

i=0

NBOC1−1∑

j=0

NBOC2−1∑

k=0

NBOC2−1∑

l=0

(−1)i+ j+k+lΛTB

(τ + (i− j)TB + (k − l) TB

NBOC2

).

(18)

Again, for SinBOC(1, 1) case, the expression of (18) reducesto

RidealSinBOC(1,1)(τ)

= (2ΛTB (τ)−ΛTB

(τ − TBOC

)−ΛTB

(τ + TBOC

)),

(19)

which is, again, similar to Julien& al. expression of (12) withthe exception of a 1/2 factor (for SinBOC(1, 1), TBOC = Tc/2,NBOC1 = 2 and NBOC2 = 1).

We remark that the difference between (16) and (18)stays in the power of −1 factor, that is, (16) stands for an ap-proximation of the sidelobe effects (no main lobe included),while (18) is the overall ACF (including both the main lobeand the side lobes). The next step consists in canceling the ef-fect of sidelobes (16) from the overall correlation (18), afternormalizing them properly.

Thus, in order to obtain an unambiguous ACF shape, thesquared function (Rideal

sin (·))2, (Ridealcos (·))2, respectively, has to

be subtracted from the ambiguous squared correlation func-tion as shown in

Ridealunamb(τ) = (Rideal

BOC(τ))2 −w(Rideal

sin / cos(τ))2

, (20)

wherew < 1 is a weight factor used to normalize the referencefunction (to achieve a magnitude of 1).

For example, for SinBOC(1, 1) and w = 1, we get from(17), (19), and (20), after straightforward computations, that

Ridealunamb(τ) = 4

(Λ2TB (τ)−ΛTB (τ)ΛTB

(τ − TBOC

)

−ΛTB (τ)ΛTB

(τ + TBOC

)),

(21)

and if we plot Ridealunamb(τ) (e.g., see the lower plot of Figure 8),

we get a main narrow correlation peak, without sidelobes.All the derivations so far were based on ideal assumptions

(ideal correlation codes, single path static channels, etc.).However, in practice, we have to cope with the real signals,so the ideal autocorrelation function Rideal

BOC(τ) should be re-placed with the computed correlation RBOC(τ) between thereceived signal and the reference BOC-modulated pseudo-random code. Thus, (20) becomes

Runamb(τ) = (RBOC(τ))2 −w(Rideal

sin / cos(τ))2. (22)

Here comes into equation the weighting factor, since vari-ous channel effects (such as noise and multipath) can mod-ify the levels of RBOC(τ) function. In order to perform the

1

0.5

0−1.5 −1 −0.5 0 0.5 1 1.5

CosBOC (10, 5) modulation, ACFs ofBOC-modulated and subtracted signals

Continue line:BOC-modulated signal

Dashed line:subtracted signal

Delay (chips)

1

0.5

0

−1.5 −1 −0.5 0 0.5 1 1.5

CosBOC (10, 5) modulation, ACF of unambiguous signal

Unambiguous signal

Delay (chips)

Figure 9: CosBOC(10, 5)-modulated signal: examples of the am-biguous correlation function and subtracted pulse (upper plot)and obtained unambiguous correlation function (lower plot), in asingle-path channel.

normalization of reference function (i.e., to find the weightfactorsw), the peaks magnitudes of RBOC(·) function are firstfound out and sorted in increased order. Then the weightingfactor w is computed as the ratio between the last-but-onepeak and the highest peak. We remark that the above algo-rithm does not require the computation of the BOC/PRNcorrelation anymore, it only requires the computation ofRBOC(τ) = Rn(τ) correlation. The pulses to be subtracted arealways based on the ideal functions Rideal

sin / cos(τ), and therefore,they can be computed only once (via (16)) and stored at thereceiver (in order to decrease the complexity of the trackingunit).

By comparison with Julien&al. method, here the num-ber of correlations at the receiver is reduced by half (i.e.,RBOC,PRN(·) computation is not needed anymore). Thus theSCM technique offers less computational burden (only onecorrelation channel in contrast to Julien&al. method, whichuses two correlation channels).

Figures 8 and 9 show the shapes of the ideal ambigu-ous correlation functions and of the subtracted pulses, to-gether with the correlation functions, obtained after subtrac-tion (SCM method). Figure 8 exemplifies a SinBOC(1, 1)-modulated signal, while Figure 9 illustrates the shapes for aCosBOC(10, 5)-modulation case. As it can be observed, forboth SinBOC and CosBOC modulations, the subtractionsremoves the sidelobes closest to the main peak, which arethe main threats in the tracking process. Also, it should bementioned that the Figure 8, for a SinBOC(1, 1) modulatedsignal, is also illustrative for the Julien&al. method, since theshapes of correlation functions are similar with those pre-sented in [20].

Equation (20) is valid for single path channels. How-ever, in multipath presence, delay errors due to multipaths


are likely to appear. When (22) is applied in this situation,one important issue is to align the subtraction pulse to theLOS peak (otherwise, the subtraction of (22) will not can-cel the correct sidelobes). This can be done only if some ini-tial estimate of LOS delay is obtained. For this purpose, weemploy and compare several feedback loops or feedforwardalgorithms, as it will be explained next.

4.2. SCM with interference cancellation (IC)

Combining the multipath eliminating DLL concept with theSCM method, we obtain an improved SCM technique withmultipath interference cancellation (SCM with IC). In thismethod, the initial estimate of LOS delay is obtained viaMEDLL algorithm. The sidelobe cancellation is applied in-side the iterative steps of MEDLL, as explained below.

(1) Calculate the correlation function Rn(τ) between thereceived signal and the reference BOC-modulatedcode (e.g., see the continuous line, Figure 10, up-per plot). Find the global maximum peak (the peak1) of this correlation function, maxτ |Rn(τ)|, and itscorresponding delay, τ1,n, amplitude a1,n and phase

θ1,n (e.g., the peak situated at the 50th-sample delay,Figure 10, upper plot).

(2) Compute the ideal reference function centered at τ1,n:Rideal

sub (τ − τ1,n) via (16) (see the dashed line, Figure 10,upper plot).

(3) Build an initial estimate of the channel impulse re-

sponse (CIR) based on τ1,n, a1,n, and θ1,n (e.g., the es-timated CIR of peak 1, Figure 10, upper plot).

(4) In order to remove the sidelobes ambiguities, thefunction Rideal

sub (τ − τ1,n) is then subtracted from themultipath correlation function Rn(τ) and an unam-biguous shape is obtained, using (22), or, equiva-lently Rn,unamb(τ) = (Rn(τ))2 − (Rideal

sub (τ − τ1,n))2. InFigure 10, the unambiguous ACF Rn,unamb(·) is plot-ted with dashed-dotted line, in both upper and lowerplots.

(5) Cancel out the contribution of the strongest path

and obtain the residual function R(1)n,unamb(τ) =

Rn,unamb(τ) − a1,nRidealunamb(τ)(τ − τ1,n)e jθ1,n , where

Ridealunmab(τ) is the unambiguous reference function

given by (20). The shape of residual function isexemplified in Figure 10, lower plot (drawn withcontinuous line).

(6) The new maximum peak of the residual functionR(1)n,unamb is found out (e.g., at 44th-sample delay,

Figure 10, lower plot), with its corresponding de-

lay τ2,n, amplitude a2,n and phase θ2,n. The con-tributions of both peaks 1 and 2 are subtractedfrom unambiguous correlation function Rn,unamb(τ)

1

0.8

0.6

0.4

0.2

0

0 10 20 30 40 50 60 70 80

Samples

Exemplification of SCM IC method (steps 1 to 4)

Original ACFEstimated CIR

Subtracted ideal functionUnambiguous ACF

1

0.8

0.6

0.4

0.2

−0.2

0

0 10 20 30 40 50 60 70 80

Samples

Exemplification of SCM IC method (steps 5 to 6)

Unambiguous ACFResidual functionEstimated CIR, 2nd peak

Figure 10: Exemplification of SCM IC method, 2-paths fadingchannel with true channel delay at 44 and 50 samples, average pathpowers [−2, 0] dB, SinBOC(1, 1)-modulated signal.

and the maximum global peak is re-estimated from

R(2)n,unamb(τ) = (Rn,unamb(τ))2 − (a1,nR

idealunamb(τ)(τ −

τ1,n)e jθ1,n + a2,nRidealunamb(τ)(τ − τ2,n)e jθ2,n)2.

(7) The steps (3) to (6) are repeated until all desired peaksare estimated and until the residual function is belowa threshold value. In the example of Figure 10, after 6steps both path delays are estimated correctly.

These steps of SCM IC method are illustrated inFigure 10, for 2-path fading channel.


1

0.8

0.6

0.4

0.2

0

−0.2

−0.4

−0.6

−0.8

−1−1.5 −1 −0.5 0 0.5 1 1.5

Nor

mal

ized

S-cu

rve

Delay error (chips)

Ideal S-curve (no multipath), SCM NEML method


Figure 11: SCM NEML method: ideal S-curves (no multipath), fortwo BOC-modulation cases and Δ = 0.1 chips.

4.3. SCM using narrow early minus lat discriminator(SCM NEML)

After obtaining an unambiguous correlation functionRn,unamb(τ) (as it was shown in the previous section, steps(1) to (4)), a NEML S-curve is constructed, by forming theearly, respectively, late branches, spaced at Δ = 0.1 chips. TheS-curve is obtained in the same way as in Section 3.1, by sub-tracting the late and early branches of unambiguous correla-tion function,

SSCMNEML (τ) = ∣∣RLaten,unamb(τ)

∣∣2 − ∣∣REarlyn,unamb(τ)

∣∣2. (23)

Examples of S-curves obtained with this method, inpresence of a single path static channel, are presented inFigure 11, for two BOC-modulated signals, SinBOC(1, 1)and SinBOC(10, 5), and a spacing of Δ = 0.1 chips. Com-paring with Figure 4, which presents the NEML S-curves forambiguous signals, in Figure 11, the possibility to detect anincorrect zero crossing, due to sidelobes peaks, is decreased.

A typical measure of performance for the ability of a de-lay tracking loop to deal with multipath error is the so-calledmultipath error envelope (MEE) [9, 10]. The MEE is usu-ally computed for one direct and one reflected channel paths,with a certain variable spacing. The multipath errors are cal-culated for the worst-case scenario, when the two paths areadded inphase (upper MEE) and have equal strength, andalso, when the two paths are out of phase (lower MEE). Com-parisons of MEEs plots, for both NEML and SCM NEMLmethods, are shown in Figure 12, for two BOC-modulatedsignals. A static channel with two paths of equal amplitudesand variable spacing was considered. The only interferenceconsidered here is the multipath interference, and the addi-tive white noise effect is not taken into account. As it can beseen in Figure 12, comparing with the NEML correlator, the

10

0

−10

0 0.2 0.4 0.6 0.8 1

Mu

ltip

ath

erro

ren

velo

pe

(met

ers)

SinBOC (1, 1), Δ = 0.1 chips

Multipath spacing (chips)

NEML correlatorSCM NEML method

10

0

−10

0 0.2 0.4 0.6 0.8 1

Mu

ltip

ath

erro

ren

velo

pe

(met

ers)



NEML correlatorSCM NEML method

Figure 12: Multipath error envelopes (in meters): NEML correlatorversus SCM NEML method, for two BOC-modulation cases andΔ = 0.1 chips.

SCM NEML method brings a decrease in the errors of mul-tipath envelopes, for both SinBOC(1, 1) and SinBOC(10, 5)signals. We remark that the variations of the lower delay er-ror envelope in the lower plot of Figure 12 are due to, on onehand, the errors in the zero-crossing estimation algorithm,and, on the other hand, to the fact that worse MEE is notnecessarily guaranteed when the paths are out of phase forthe noncoherent NEML.

4.4. SCM using high-resolution correlatordiscriminator (SCM HRC)

In a similar manner as in previous section, the SCM methodcan be also used in conjunction with an HRC discrimina-tor, after removing the side peaks threats and obtaining anunambiguous correlation function Rn,unamb(τ). Based on thisunambiguous function, an HRC S-curve is constructed, in ananalogous way as in Section 3.2:

SSCMHRC (τ) = ∣∣RLaten,unamb(τ)

∣∣2 − ∣∣REarlyn,unamb(τ)

∣∣2

+ a(∣∣RVeryLate

n,unamb(τ)∣∣2 − ∣∣RVeryEarly

n,unamb (τ)∣∣2)

,

(24)

where REarlyn,unamb(·) and RLate

n,unamb(·) are the advanced and de-layed unambiguous correlations, with a spacing between

them of Δ = 0.1 chips. The RVeryEarlyn,unamb (·), respectively,

RVeryLaten,unamb(·) are the very early and the very late unambiguous

correlation branches, spaced at 2Δ chips and the weightingfactor a = −1/2.


1

0.8

0.6

0.4

0.2

0

−0.2

−0.4

−0.6

−0.8

−1−1.5 −1 −0.5 0 0.5 1 1.5

Nor

mal

ized

S-cu

rve

Delay error (chips)

Ideal S-curve (no multipath), SCM HRC method


Figure 13: SCM HRC method: ideal S-curves (no multipath), fortwo BOCmodulation cases, with a = −1/2 and Δ = 0.1 chips.

10

5

0

−5

−10

0 0.2 0.4 0.6 0.8 1

Mu

ltip

ath

erro

ren

velo

pe

(met

ers)



HRC methodSCM HRC method

10

50

−5

−10

0 0.2 0.4 0.6 0.8 1

Mu

ltip

ath

erro

ren

velo

pe

(met

ers)



HRC methodSCM HRC method

Figure 14: Multipath error envelopes (in meters): HRC methodversus SCM HRC method, for two BOC-modulation cases andΔ = 0.1 chips.

The ideal S-curves obtained with the SCM HRC method,for two BOC-modulation orders, are presented in Figure 13.The MEEs performances, for both the HRC and SCM HRCmethods, are illustrated in Figure 14, for SinBOC(1, 1) and

0.8

0.6

0.4

0.2

0

−0.2

−1.5 −1 −0.5 0 0.5 1 1.5

Nor

mal

ized

AC

F

Delay error (chips)

Ideal ACF (no multipath) for SinBOC (10, 5) modulated signal

Ambiguous correlationDifferential correlation

SCM methodSCM DC method

Figure 15: Envelopes of correlation functions obtained with am-biguous correlation, DC method, SCM approach, and SCM DCmethod, for a SinBOC(10, 5)-modulated signal.

SinBOC(10, 5) cases. As it can be noticed, there is a slight im-provement brought by the SCM HRC method over the HRCcorrelator.

4.5. SCM using differential correlation (DC) inconjunction with feedback and feedforwardtracking algorithms

It has been observed that the DC method has potential to de-crease the sidelobes amplitudes, thus lowering the possibilityto detect a wrong side peak. To enhance the performance ofthe DC method, we use it in conjunction with different track-ing algorithms, such as NEML or HRC methods, or with ICmethod. These algorithms are applied in similar ways as ex-plained in Sections 3.1, 3.2, and 3.3, on the correlation func-tions obtained after performing the noncoherent DC tech-nique (Section 3.4).

Also, the performance may be enhanced further, by us-ing the SCM approach after applying the DC method. This isdone in the same way as explained in previous Sections (4.2,4.3, and 4.4), but after using first the DC method on the am-biguous correlation function between the multipath receivedsignal and the reference BOC-modulated code. Indeed, as il-lustrated in Figure 15, in case of a SinBOC(10, 5) modulatedsignal, the combination of DC and SCM algorithms can de-crease even further the sidelobes amplitudes, thus eliminat-ing more ambiguities.

4.6. SCM with threshold comparison (SCM thr)

Another approach is to test the performance of SCM tech-nique using a thresholding algorithm. Starting from the un-ambiguous correlation function Rn,unamb(τ), an estimate ofnoise variance σ2

n is obtained, as the mean of the squares of


the out-of-peak values, similar to [4]. Using this estimatednoise variance, a linear threshold γ is computed, based on thesecond peak γ2 of the ideal unambiguous correlation func-tion Rideal

unamb(τ) (i.e., for SinBOC(1, 1) γ2 = 0.5, as seen inFigure 3), together with the estimate of the noise variance σ2

n :

γ = γ2 +√σ2n . (25)

Then the LOS delay is estimated, based on the unambigu-ous correlation function Rn,unamb(τ), using this threshold. Ifthe peak of the estimated first path is too low (i.e., ten timeslower than the global peak), then this path is discarded andthe next estimate is considered.

5. SIMULATION RESULTS

5.1. Additive white noise Gaussian (AWGN) channel

We first test the performance of the proposed algorithms inthe ideal AWGN channel (single path), in order to checkwhether SCM algorithm introduces a deterioration with re-spect to the standard narrow and high-resolution correla-tors (it is known that NEML is able to attain the Cramer-Rao bound in AWGN channels [8]). We will show that nodeterioration is incurred when SCM is applied. The perfor-mance criteria are root mean square error (RMSE) and meantime to lose lock (MTLL). The simulations were carried outin Matlab. The MTLL is computed as the average value forwhich the estimated delay tracking error of the first pathis below 1 chip. The tracking process is started, after thecoarse acquisition of the signal, assuming that we are in the“lock” condition, that is, the delay error is strictly less thanone chip. For all presented simulations (both in this sectionand in Section 5.2), the coherent integration length is set toNc = 20 milliseconds and the noncoherent integration is per-formed over Nnc = 3 blocks (i.e., the total coherent and non-coherent integration length is 60 milliseconds), and the over-sampling factor is set to Ns = 11. We generated 5000 randompoints in order to compute the RMSE and MTLL statistics.That is, the maximum observable MTLL based on these sim-ulations is 5000NcNnc = 300 s (i.e., an MTTL value of 300seconds reflects the fact that we never lost the lock duringthat particular simulation).

The AWGN results are shown for SinBOC(1, 1) case inFigures 16 and 17, for the comparison with NEML and HRC,respectively. As seen in these figures, SCM algorithm does notdeteriorate the performance in AWGN case, compared withnarrow and high-resolution correlators. The sidelobe cancel-lations applied on the top of NEML and HRC give the sameresults as those of the original NEML and HRC algorithms,respectively, if the channel is single path AWGN channel (e.g.,the differences in performance between SCM + NEML andNEML are only at the third decimal, with NEML slightly bet-ter).

5.2. Fading channels

In what follows, the performance of the discussed delay es-timation algorithms is compared in multipath fading chan-

RM

SE(c

hip

s)

SinBOC (1, 1), AWGN single-path channel

20 25 30 35 4010−6

10−5

10−4

10−3

10−2

10−1

100

CNR (dB-Hz)

NEMLJulien & al. EMLPSCM NEML

DC NEMLDC SCM NEML

MT

LL(s

)SinBOC (1, 1), AWGN single-path channel

20 25 30 35 40

102.4

102.3

102.2

CNR (dB-Hz)


DC NEMLDC SCM NEML

Figure 16: Comparison of feedback delays estimation algorithmsemploying the NEML discriminator and of the Julien&al. method,as a function of CNR; upper plots: RMSE, lower plots: MTLL.NEML and SCM NEML curves are overlapping. DC NEML and DCSCM NEML curves are also overlapping (differences at the 3rd dec-imal).

nels. The same performance criteria as in the previous sec-tion are used, namely, RMSE and MTLL. Two representativeBOC-modulated signals have been selected for the simula-tions included in this paper. The first one is the SinBOC(1, 1)modulation, the common baseline for Galileo open service(OS) structure, agreed by US and European negotiation.The second one is the CosBOC(10, 5) modulation, whichhas been proposed for the Galileo Public Regulated Service(PRS) and for the current GPS M-code. In order to have fair

14 EURASIP Journal on Wireless Communications and NetworkingR

MSE

(ch

ips)


20 25 30 35 4010−5

10−4

10−3

10−2

10−1

100

CNR (dB-Hz)

HRCJulien & al. DPSCM HRC

DC HRCSCM DC HRC

MT

LLS

(s)


20 22 24 26 28 30 32 34 36 38

100

200

350

CNR (dB-Hz)


DC HRCSCM DC HRC

Figure 17: Comparison of feedback delays estimation algorithmsemploying the HRC discriminator and of the Julien&al. method,as a function of CNR, upper plots: RMSE, lower plots: MTLL. HRCand SCM HRC curves are overlapping; DC HRC and DC SCM HRCcurves are also overlapping (differences at the 4th decimal).

comparison, the performance of introduced feedback tech-niques is evaluated separately from that of the feedforwardmethods. The same modulation types as in Section 5.1 areused here, namely, SinBOC(1, 1) and CosBOC(10, 5) mod-ulations. However, the introduced SCM method can be ex-tended to any sine or cosine BOC-modulation case.

The studied techniques have been investigated under theassumption of indoor or outdoor Rayleigh or Rician multi-path profiles (i.e., for indoor channel, the speed mobile is set

to v = 3 km/h, while for outdoor profiles, the mobile speedsof 25, 45, or 75 km/h have been selected). Two main chan-nel profiles have been considered: either with fixed Rayleighdistribution of all paths and with average path power of −1,−2, 0 and −3 dB, or a 2-paths decaying power delay profile(PDP) channel, with Rician distributions for the first pathand Rayleigh distribution for the next path. Similar with theAWGN case in Section5.1, during simulations, the first pathdelay of the channel is assumed to be linearly increasing, witha slope of 0.05 chips per block of NcNnc millisecond, thus thetracking algorithms should capture this linear delay increase.The successive channel path delays have a random spacingwith respect to the precedent delay, uniformly distributed be-tween 1/(NsNBOC1NBOC2 ) and xmax, where xmax (in chips) isthe maximum separation between successive paths (i.e., forclosed-spaced paths scenario, xmax = 0.1 chips). In order tohave independent and reliable results for each method, thesearch interval is different for each algorithm. which meansthat once the lock is lost for one method, this will not affectthe other algorithms. The search window has few chips (typ-ically between 4 and 12 chips), depending on the numberof paths, the distance between them and on the used BOC-modulation orders. The search window is sliding around theprevious delay estimate and if we have erroneous estimates,the lock is lost at some point. For the feedback algorithms(i.e., NEML, HRC, or Julien&al. methods), the search forzero crossing is conditioned by the previous delay estimates.Similar with AWGN case, he coherent integration length isset to Nc = 20 milliseconds, the noncoherent integration isperformed over Nnc = 3 blocks, and the oversampling factoris set to Ns = 11.

The SCM approach is exemplified in Figure 18, for aRayleigh 2-paths fading channel, with equal PDP. The up-per plot exemplifies a SinBOC(1, 1) modulation case, withxmax = 1 chip, while the lower plot shows the original ACF,together with subtracted pulse and unambiguous shape, fora SinBOC(10, 5) case and xmax = 0.5 chips. In both casesthe threat of the sidelobes is eliminated using the SCM tech-nique. For instance, in the SinBOC(1, 1) case, the correct de-lay of first path, situated at the 70th sample (in one chip, thereare NsNBOC1NBOC2 samples) is more likely to be detected, af-ter the main sidelobe (situated at the 81th sample) is removedby subtraction.

Figure 19 presents the RMSE and MTLL, for the feedbackalgorithms which use the NEML discriminator, with an earlylate spacing of Δ = 0.1 chips. The signal is SinBOC(1, 1)modulated. Here, the Julien&al. method employs an EMLPdiscriminator, as presented in Section 3.5. The channel is 4-path outdoor Rayleigh channel, v = 75 km/h, with the mostchallenging situation of closely-spaced paths (i.e., xmax = 0.1chips). From both plots, it can be seen that both SCM-enhanced methods (the SCM NEML and SCM DC NEML)are performing much better than the other algorithms. Also,the Julien&al. EMLP technique brings an improvement in theresults, comparing with both NEML and DC NEML meth-ods, but still not approaching the performance of the SCMalgorithms.


0.8

0.6

0.4

0.2

0

−0.2

40 60 80 100 120

AC

Fs

Delay error (samples)

SinBOC (1, 1), Rayleigh fading channelwith 2 paths, xmax = 1 chip

Ambiguous ACFSubtracted pulseUnambiguous ACF

1st path true delay =70 samples

0.8

0.6

0.4

0.2

0

−0.2

180 200 220 240 260 280 300 320

AC

Fs

Delay error (samples)

SinBOC (10, 5), Rayleigh fading channelwith 2 paths, xmax = 0.5 chips

Ambiguous ACFSubtracted pulseUnambiguous ACF

True delay =239 samples

1

Figure 18: Exemplification of SCM method for a 2-paths Rayleighfading channel. Upper plot: SinBOC(1, 1)-modulated signal andxmax = 1 chip. Lower plot: SinBOC(10, 5)-modulated signal andxmax = 0.5 chips.

Figures 20 and 21 illustrate the performances of theintroduced methods using an HRC discriminator. TheJulien&al. method employs a DP discriminator, as explainedin Section 3.5. This selection is done because it has been ob-served by simulations that the Julien&al. method employinga DP discriminator exceeds the performance of the EMLPdiscriminator; this behavior is expected since the DP ap-

RM

SE(c

hip

s)

SinBOC (1, 1), Rayleigh channel,speed mobile = 75 km/h, xmax = 0.1 chips

20 25 30 35 40

10−0.6

10−0.5

10−0.4

10−0.3

CNR (dB-Hz)


DC NEMLSCM DC NEML

MT

LL(s

)

SinBOC (1, 1), Rayleigh channel, 4 paths, xmax = 0.1 chips

20 25 30 35 40

102

CNR (dB-Hz)


DC NEMLSCM DC NEML

Figure 19: Comparison of feedback delays estimation algorithmsemploying the NEML discriminator and of the Julien&al. method,as a function of CNR; SinBOC(1, 1) modulation, Rayleigh channelwith an average pathspower delay profile of −1, −2, 0, and −3 dB,v = 75 km/h, closely spaced paths with xmax = 0.1 chips.

proach does not vary linearly with the code tracking error[20] as the EMLP discriminator. In Figure 20, the signal isSinBOC(1, 1)-modulated, for a 2-path channel with Riciandistribution for the first path, a mobile speed of 25 km/h anda large separation between successive paths xmax = 1 chip.Figure 21 presents the case of a CosBOC(10, 5)-modulated


MSE

(ch

ips)

SinBOC (1, 1), 2-paths Rician channel,xmax = 1 chip, mobile speed = 25 km/h

20 25 30 35 40

10−0.5

10−0.4

10−0.3

CNR (dB-Hz)


DC HRCSCM DC HRC

MT

LL(s

)

SinBOC (1, 1), 2-paths Rician channel,xmax = 1 chip, mobile speed = 25 km/h

20 25 30 35 40

101

CNR (dB-Hz)


DC HRCSCM DC HRC

Figure 20: Comparison of feedback delays estimation algorithmsemploying the HRC discriminator and of the Julien&al. method, asa function of CNR; SinBOC(1, 1) modulation, 2-paths Rician chan-nel with decaying PDP of 0 and −2 dB, v = 25 km/h, maximumseparation between paths xmax = 1 chip.

signal, for a 4-paths Rayleigh channel, with closely spacedpaths xmax = 0.1 chips and v = 45 km/h.

From all plots of Figures 20 and 21, it can be ob-served that, in both RMSE and MTLL terms, there is asmall improvement brought by the DC HRC and SCM DCHRC methods, which have similar performance. For theSinBOC(1, 1) case, the performance of the Julien& al. DP

RM

SE(c

hip

s)

CosBOC (10, 5), Rayleigh channel,xmax = 0.1 chips, mobile speed = 45 km/h

20 25 30 35 40

10−0.6

10−0.7

10−0.5

10−0.4

10−0.3

CNR (dB-Hz)


DC HRCSCM DC HRC

MT

LL(s

)

CosBOC (10, 5), 4-paths Rayleigh channel,xmax = 0.1 chips

20 25 30 35 40

101

CNR (dB-Hz)


DC HRCSCM DC HRC

Figure 21: Comparison of feedback delays estimation algorithmsemploying the HRC discriminator and of the Julien&al. method, asa function of CNR; CosBOC(10, 5) modulation, 4-paths Rayleighchannel, with paths PDP of −1, −2, 0, and −3 dB, v = 45 km/h,closely spaced paths xmax = 0.1 chips.

method exceeds those of HRC and SCM HRC algorithms,which both give similar results. On the other hand, for theCosBOC(10, 5) modulation, the Julien& al. DP method ap-proaches the results provided by the HRC and SCM HRCalgorithms, which still offer a deterioration in performanceof about 1 dB, comparing to DC HRC and SCM DC HRCmethods.

Adina Burian et al. 17R

MSE

(ch

ips)

SinBOC (1, 1), Rayleigh channel,speed mobile = 3 km/h, xmax = 0.1 chips

20 25 30 35 40

10−0.7

10−0.9

10−0.5

10−0.3

CNR (dB-Hz)

MEDLLSCM ICSCM thr.

DC ICSCM DC IC

MT

LL(s

)

SinBOC (1, 1), Rayleigh channel,4 paths, xmax = 0.1 chips

20 25 30 35 40100

101

CNR (dB-Hz)

MEDLLSCM ICSCM thr.

DC ICSCM DC IC

Figure 22: Comparison of feedforward delays estimation algo-rithms employing the MEDLL and IC methods and of the SCMwith threshold approach, as a function of CNR; SinBOC(1, 1) mod-ulation, 4-paths indoor Rayleigh channel, with PDP of −1, −2, 0,and −3 dB, v = 3 km/h, closely spaced paths with xmax = 0.1 chips.

The comparisons between the introduced feedforwarddelay estimation algorithms (the MEDLL method, the IC en-hanced techniques and the SCM with threshold comparisonapproach) are presented in Figures 22 to 25. In Figure 22,the signal is SinBOC(1, 1)-modulated, with a indoor closelyspaced paths Rayleigh channel (xmax = 0.1 chips, v =3 km/h). In Figure 23, the signal is also SinBOC(1, 1) modu-lated, the channel is 2-paths with Rician distribution on firstpath, v = 45 km/h and xmax = 0.5 chips.

RM

SE(c

hip

s)

SinBOC (1, 1), 2-paths Rician channel,xmax = 0.5 chips, mobile speed = 45 km/h

20 25 30 35 40

10−1

100

CNR (dB-Hz)

MEDLLSCM ICSCM thr.

DC ICSCM DC IC

MT

LL(s

)SinBOC (1, 1), 2-paths Rician channel,

xmax = 0.5 chips, mobile speed = 45 km/h

20 25 30 35 40

101

102

100

CNR (dB-Hz)

MEDLLSCM ICSCM thr.

DC ICSCM DC IC

Figure 23: Comparison of feedforward delays estimation algo-rithms employing the MEDLL and IC methods and of the SCM withthreshold approach, as a function of CNR; SinBOC(1, 1) modula-tion, 2-paths decaying PDP Rician channel, v = 45 km/h, xmax = 0.5chips.

In all plots the performance of MEDLL algorithm is ex-ceeded by the other methods, since they eliminate or de-crease the threats of the sidelobes. In terms of RMSE, for aRayleigh profile with closely-spaced paths (Figure 22, upperplot), the performances of the SCM IC and DC IC algorithmsare exceeded by those of SCM DC IC and SCM thresholdingmethods, for a CNR range from 20 to 30 dB-Hz. In case ofFigure 23, for a higher spacing between successive paths up


MSE

(ch

ips)

CosBOC (10, 5), Rayleigh channel,speed mobile = 3 km/h, xmax = 0.1 chips

20 25 30 35 40

10−0.6

10−0.8

10−0.7

10−0.5

10−0.4

10−0.3

CNR (dB-Hz)

MEDLLSCM ICSCM thr.

DC ICSCM DC IC

MT

LL(s

)

CosBOC (10, 5), 4-paths Rayleigh channel,xmax = 0.1 chips

20 25 30 35 40

101

102

100

CNR (dB-Hz)

MEDLLSCM ICSCM thr.

DC ICSCM DC IC

Figure 24: Comparison of feedforward delays estimation algo-rithms employing the MEDLL and IC methods and of the SCM withthreshold approach, as a function of CNR; CosBOC(10, 5) modula-tion, 4-paths indoor Rayleigh channel, v = 3 km/h, closely-spacedpaths xmax = 0.1 chips.

to 0.5 chips and a higher mobile speed, the SCM with thresh-old comparison gives the best results, while the SCM IC andSCM DC IC methods have similar performance, which isstill better then that of DC IC, for a range of about 20 to33 dB-Hz.

In terms of MTLL, from both Figure 22 and Figure 23,lower plots, can be concluded that the best performance

MT

LL(s

)

CosBOC (10, 5), Rician channel, 2 paths, xmax = 0.5 chips

20 25 30 35 40

101

102

100

10−1

CNR (dB-Hz)

MEDLLSCM ICSCM thr.

DC ICSCM DC IC

Figure 25: Comparison of feedforward delays estimation algo-rithms employing the MEDLL and IC methods and of the SCM withthreshold approach, as a function of CNR; CosBOC(10, 5) modula-tion, 2-paths decaying PDP Rician channel, v = 45 km/h, xmax = 0.5chips.

(i.e., the highest MTLL) is provided by the SCM DC ICand SCM thresholding algorithms, with an improvement ofabout 4-5 dB-Hz comparing to SCM IC and DC IC methods,which give similar results.

Figures 24 and 25 illustrate the obtained simulation re-sults, for a CosBOC(10, 5)-modulated signals, for a 4-closely-spaced paths indoor Rayleigh profile, respectively for a 2-paths channel, with v = 45 km/h and a separation betweenpaths xmax of up to 0.5 chips. In terms of RMSE (Figure 24,upper plot), the SCM DC IC method gives the best results,followed by the SCM with threshold comparison and SCMIC methods, for a CNR range of up to 33 dB-Hz. The goodperformance of SCM DC IC method is expected, since for ahigher BOC-modulation order, it eliminates more sidelobesthan the other SCM methods (as illustrated in Figure 15).The MEDLL technique is still outperformed by all the othermethods.

In terms of MTLL (Figure 24, lower and plot andFigure 25), for both channel profile cases, the SCM withthreshold comparison and SCM DC IC approaches havethe best performance, while the SCM IC technique bringsan improvement over the DC IC case (in contrast with theSinBOC(1, 1) situation, i.e., Figure 22). This is explicable,since the SCM approach removes completely the sidelobessituated near the main peak, while the DC method just de-creases their amplitudes (Figure 15).

Figure 26 presents the effect of maximum separation be-tween successive paths xmax, in case of feedback delay esti-mation algorithms which use NEML discriminator, togetherwith the Julien&al. EMLP method. The channel has a 4-pathsindoor Rayleigh profile with the mobile speed of 4 km/h and

Adina Burian et al. 19R

MSE

(ch

ips)

SinBOC (1, 1), 4-paths Rayleigh channel,CNR = 35 dBHz, v = 4 km/h

0 0.5 1 1.5 2

10−0.6

10−0.7

10−0.5

10−0.4

10−0.3

xmax (chips)


DC NEMLSCM DC NEML

Figure 26: Comparison of feedback delays estimation algorithmsemploying the NEML discriminator and of the Julien&al. EMLPmethod, as a function of separation between successive channelpaths xmax, in terms of RMSE; SinBOC(1, 1) modulation, 4-pathsRayleigh channel, mobile speed 4 km/h, CNR = 35 dB-Hz.

the CNR is set to 35 dB-Hz. In this case, both SCM algo-rithms provide a decreasing in error as xmax is increasing,while the other methods have an almost linear behavior, forxmax greater than half of chip. Also, it can be observed that thesame gap between the studied methods, at xmax = 0.1 chips,is presented in Figure 19, upper plot.

6. CONCLUSIONS

A new tracking technique (the sidelobes cancellationmethod) has been introduced, which removes or dimin-ishes the sidelobes ambiguities of the BOC-modulated sig-nals, while keeping the narrow width of the main lobe, whichis benefic for the tracking process. In contrast with othermethods, this algorithm has the advantage that can be ap-plied to any sine or cosine, odd or even BOC-modulationcase. It also provides a lower complexity solution, since ituses ideal reference correlation functions, which are gener-ated only once and can be stored at receiver side. The per-formance of the SCM algorithm can be enhanced if othertracking-loop methods are used after removing the sidelobesand the multipath problem can be alleviated, since the un-desired effect of short delay multipath can be reduced. Ithas been shown through extensive simulation results, that incase of multipath fading channels, with both closely spacedor long delayed paths, the introduced SCM algorithms bringan improvement in performance compared to other consid-ered delay tracking methods. The highest performance im-provement comes when combining SCM technique with thenarrow EML correlator. The combination between HRC and

SCM does not bring substantial improvement, since HRChas already rather good performance in multipath channels.Also, the higher BOC-modulation order, the more advanta-geous is to apply SCM technique in order to cope better withthe false lock points.

ACKNOWLEDGMENTS

This work was carried out in the project “Advanced Tech-niques for Personal Navigation (ATENA)” funded by theFinnish Funding Agency for Technology and Innovation(Tekes). This work has also been supported by the Academyof Finland. The authors would like to thank the anonymousreviewers for their valuable comments to improve this paper.

REFERENCES

[1] J. Betz and D. Goldstein, “Candidate designs for an ad-ditional civil signal in GPS spectral bands,” Tech. Rep.,MITRE, Bedford, Mass, USA, 2002. http://www.mitre.org/work/tech papers/tech papers 02/betz candidate/.

[2] B. Barker, J. Betz, J. Clark, et al., “Overview of the GPS Mcode signal,” in CDROM Proceedings of the ION National Meet-ing; Navigating into the New Millennium, Anaheim, Calif, USA,January 2000.

[3] GJU, “Galileo Open Service—Signal in Space Interface Con-trol Document (OS SIS ICD),” Galileo Joint Undertalikng(GJU), http://www.galileoju.com/, May 2006.

[4] E. S. Lohan, A. Lakhzouri, and M. Renfors, “Feedforward delayestimators in adverse multipath propagation for Galileo andmodernized GPS signals,” EURASIP Journal on Applied SignalProcessing, vol. 2006, Article ID 50971, 19 pages, 2006.

[5] J. Betz, “The offset carrier modulation for GPS moderniza-tion,” in Proceedings of the National Technical Meeting of the In-stitute of Navigation (ION-NTM ’99), pp. 639–648, San Diego,Calif, USA, January 1999.

[6] J. Betz, “Design and performance of code tracking for the GPSM code signal,” Tech. Rep., MITRE, Mclean, Va, USA, Septem-ber 2000, http://www.mitre.org/work/tech papers/tech pa-pers 00/betz codetracking/.

[7] J. Holmes, S. Raghavan, and S. Lazar, “Acquisition and track-ing performance of NRZ and square wave modulated symbolsfor use in GPS,” in Proceedings of the 54th Annual Meeting of theInstitue of Navigation, pp. 611–625, Denver, Colo, USA, June1998.

[8] A. V. Dierendonck, P. Fenton, and T. Ford, “Theory and per-formance of narrow correlator spacing in a GPS receiver,” Jour-nal of the Institute of Navigation, vol. 39, no. 3, pp. 265–283,1992.

[9] M. Irsigler and B. Eissfeller, “Comparison of multipath mit-igation techniques with consideration of future signal struc-tures,” in Proceedings of the International Technical Meetingof the Institute of Navigation (ION-GPS/GNSS ’03), pp. 2584–2592, Portland, Ore, USA, September 2003.

[10] A. McGraw and M. Braasch, “GNSS multipath mitigationusing high resolution correlator concepts,” in Proceedings ofthe National Technical Meeting of the Institute of Navigation(ION-NTM ’99), pp. 333–342, San Diego, Calif, USA, January1999.

[11] L. Garin and J.-M. Rousseau, “Enhanced strobe correlatormultipath rejection for code and carrier,” in Proceedings of the10th International Technical Meeting of the Satellite Division of


the Institute of Navigation (ION-GPS ’97), vol. 1, pp. 559–568,Kansas City, Mo, USA, September 1997.

[12] J. Jones, P. Fenton, and B. Smith, “Theory and perfor-mance of the pulse aperture correlator,” Tech. Rep., NovA-tel, Calgary, Alberta, Canada, September 2004, http://www.novatel.com/Documents/Papers/PAC.pdf.

[13] A. V. Dierendonck and M. Braasch, “Evaluation of GNSS re-ceiver correlation processing techniques for multipath andnoise mitigation,” in Proceedings of the National TechnicalMeeting of the Institute of Navigation (ION-NTM ’97), pp.207–215, Santa Monica, Calif, USA, January 1997.

[14] C. Lee, S. Yoo, S. Yoon, and S. Y. Kim, “A novel multipathmitigation scheme based on slope differential of correlatoroutput for Galileo systems,” in Proceedings of the 8th Inter-national Conference on Advanced Communication Technology(ICACT ’06), vol. 2, pp. 1360–1363, Phoenix Park, Korea,February 2006.

[15] R. van Nee, J. Siereveld, P. Fenton, and B. Townsend, “Themultipath estimating delay lock loop: approaching theoreti-cal accuracy limits,” in Proceedings of IEEE Position Locationand Navigation Symposium, pp. 246–251, Las Vegas, Nev, USA,April 1994.

[16] P. A. Bello and R. L. Fante, “Code tracking performance fornovel unambiguous M-code time discriminators,” in Proceed-ings of the National Technical Meeting of the Institute of Nav-igation (ION-NTM ’05), pp. 293–298, San Diego, Calif, USA,January 2005.

[17] P. Fine and W. Wilson, “Tracking algorithms for GPS offsetcarrier signals,” in Proceedings of the National Technical Meet-ing of the Institute of Navigation (ION-NTM ’99), San Diego,Calif, USA, January 1999.

[18] V. Lin, P. Dafesh, A. Wu, and C. Cahn, “Study of the impactof false lock points in subcarrier modulated ranging signalsand recommended mitigation approaches,” in Proceedings ofthe 59th ION Annual Meeting & CIGTF Guidance Test Sympo-sium, pp. 156–165, Albuquerque, NM, USA, June 2003.

[19] P. Ward, “A design technique to remove the correlation ambi-guity in binary offset carrier (BOC) spread spectrum signals,”in Proceedings of the National Technical Meeting of the Instituteof Navigation (ION-NTM ’04), pp. 886–896, San Diego, Calif,USA, January 2004.

[20] O. Julien, C. Macabiau, M. Cannon, and G. Lachapelle, “BOCsignal acquisition and tracking method and apparatus,” USPatent Application Publication 2005/0270997 A1, December2005.

[21] V. Heiries, J.-A. Avila-Rodriguez, M. Irsigler, G. Hein, E. Re-beyrol, and D. Roviras, “Acquisition performance analysis ofcomposite signals for the L1 OS optimized signal,” in Proceed-ings of the 18th International Technical Meeting of the Satel-lite Division of the Institue of Navigation (ION-GNSS ’05), pp.877–889, Long Beach, Calif, USA, September 2005.

[22] A. Schmid and A. Neubauer, “Differential correlationfor Galileo/GPS receivers,” in Proceedings IEEE Interna-tional Conference on Acoustics, Speech, and Signal Processing(ICASSP ’05), vol. 3, pp. 953 –956, Philadelphia, Pa, USA,March 2005.

[23] A. Burian, E. S. Lohan, and M. Renfors, “Sidelobe cancellationmethod for unambiguous tracking of binary-offset-carriermodulated signals,” in CDROM Proceedings of the 3rd ESAWorkshop on Satellite Navigation User Equipment Technolo-gies (NAVITEC ’06), Noordwijk, The Netherlands, December2006.

[24] G. Hein, J. Godet, J.-L. Issler, J. C. Martin, T. Pratt, and

R. Lucas, “Status of Galileo frequency and signal design,”in CDROM Proceedings of the International Technical Meet-ing of the Satellite Division of the Institute of Navigation(ION-GPS ’02), Portland, Ore, USA, September 2002.

[25] E. S. Lohan, A. Lakhzouri, and M. Renfors, “Binary-offset-carrier modulation techniques with applications in satel-lite navigation systems,” Wireless Communications and MobileComputing, vol. 7, no. 6, pp. 767–779, 2006.

[26] E. Rebeyrol, C. Macabiau, L. Lestarquit, et al., “BOC powerspectrum densities,” in CDROM Proceedings of the NationalTechnical Meeting of Institute of Navigation (ION-NTM ’05),San Diego, Calif, USA, January 2005.


Research ArticleAnalysis of Filter-Bank-Based Methods for Fast SerialAcquisition of BOC-Modulated Signals

Elena Simona Lohan

Institute of Communications Engineering, Tampere University of Technology, P.O. Box 553, 33101 Tampere, Finland

Received 29 September 2006; Accepted 27 July 2007


Binary-offset-carrier (BOC) signals, selected for Galileo and modernized GPS systems, pose significant challenges for the code ac-quisition, due to the ambiguities (deep fades) which are present in the envelope of the correlation function (CF). This is differentfrom the BPSK-modulated CDMA signals, where the main correlation lobe spans over 2-chip interval, without any ambiguities ordeep fades. To deal with the ambiguities due to BOC modulation, one solution is to use lower steps of scanning the code phases(i.e., lower than the traditional step of 0.5 chips used for BPSK-modulated CDMA signals). Lowering the time-bin steps entailsan increase in the number of timing hypotheses, and, thus, in the acquisition times. An alternative solution is to transform theambiguous CF into an “unambiguous” CF, via adequate filtering of the signal. A generalized class of frequency-based unambigu-ous acquisition methods is proposed here, namely the filter-bank-based (FBB) approaches. The detailed theoretical analysis ofFBB methods is given for serial-search single-dwell acquisition in single path static channels and a comparison is made with otherambiguous and unambiguous BOC acquisition methods existing in the literature.

Copyright © 2007 Elena Simona Lohan. This is an open access article distributed under the Creative Commons AttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properlycited.

1. INTRODUCTION

The modulation selected for modernized GPS and Galileosignals is BOC modulation, often denoted as BOC(m,n),with m = fsc/ fref, n = fc/ fref. Here, fc is the chip rate, fsc

is the subcarrier rate, and fref = 1.023 MHz is the referencechip frequency (that of the C/A GPS signal) [1]. Alterna-tively, a BOC-modulated signal can also be defined via itsBOC modulation order NBOC � 2 fsc/ fc [2–4]. Both sine andcosine BOC variants are possible (for a detailed descriptionof sine and cosine BOC properties, see [3, 4]). The acqui-sition of BOC-modulated signals is challenged by the pres-ence of several ambiguities in CF envelope (here, CF refers tothe correlation between the received signal and the referenceBOC-modulated code). That is, if the so-called ambiguous-BOC (aBOC) approach [5–7] is used (meaning that thereis no bandlimiting filtering at the receiver or that this filterhas a bandwidth sufficiently high to capture most energy ofthe incoming signal), the resultant CF envelope will exhibitsome deep fades within ±1 chip interval around the correctpeak [5, 8], as it will be illustrated in Section 4. We remarkthat sometimes the term “ambiguities” refers to the multi-ple peaks within ±1 chip interval around the correct peak;

however, they are also related to the deep fades within thisinterval. The terminology used here refers to the deep fadesof CF envelope.

The number of fades or ambiguities within 2-chip inter-val depends on the NBOC order (e.g., for SinBOC, we have2NBOC− 2 ambiguities around the maximum peak, while forCosBOC, we have 2NBOC ambiguities [4]). The distance be-tween successive ambiguities in the CF envelope sets an up-per bound on the step of searching the time-bin hypotheses(Δt)bin, in the sense that if the time-bin step becomes toohigh, the main lobe of the CF envelope might be lost duringthe acquisition. Typically, a step of one-half the distance be-tween the correlation peak and its first zero value, or, equiva-lently, one quarter of the main lobe width is generally consid-ered [9]. For example, acquisition time-bin steps of 0.5 chipsare used for BPSK modulation (such as for C/A code of GPS),where the width of the main lobe is 2 chips, and steps of 0.1–0.2 chips are used for SinBOC(1,1) modulation, where thewidth of the main lobe is about 0.7 chips (such as for GalileoOpen Service) [5, 10, 11].

In order to be able to increase the time-bin step (and,thus, the speed of the acquisition process), several Filter-Bank-Based (FBB) methods are proposed here, which exploit


Time uncertainty Δtmax

...... · · ·

· · ·

· · ·

(Δf)

bin

Time-bin step (Δt)bin

Freq

uen

cyu

nce

rtai

ntyΔf m

ax

One time-frequency bin

Figure 1: Illustration of the time/frequency search space.

the property that by reducing the signal bandwidth beforecorrelation, we are able to increase the width of the CFmain lobe. A thorough theoretical model is given for thecharacterization of the decision variable in single-path staticchannels and the theoretical model is validated via sim-ulations. The proposed FBB methods are compared withtwo other existing methods in the literature: the classicalambiguous-BOC processing (above-mentioned) and a morerecent, unambiguous-BOC technique, introduced by Fish-man and Betz [9] (denoted here via B&F method, but alsoknown as sideband correlation method or BPSK-like tech-nique) and further analyzed and developed in [2, 6, 7, 10, 11].It is mentioned that FBB methods have also been studied bythe author in the context of hybrid-search acquisition [12].However, the theoretical analysis of FBB methods is newlyintroduced here.

2. ACQUISITION PROBLEM AND AMBIGUOUS(ABOC) ACQUISITION

In Global Navigation Satellite Systems (GNSS) based on codedivision multiple access (CDMA), such as Galileo and GPSsystems, the signal acquisition is a search process [13] whichrequires replication of both the code and the carrier of thespace vehicle (SV) to acquire the SV signal. The range di-mension is associated with the replica code and the Dopplerdimension is associated with the replica carrier. Therefore,the signal match is two dimensional. The combination ofone code range search increment (code bin) and one velocitysearch increment (Doppler bin) is a cell.

The time-frequency search space is illustrated in Figure 1.The uncertainty region represents the total number of cells(or bins) to be searched [13–15]. The cells are tested by cor-relating the received and locally generated codes over a dwellor integration time τd. The whole uncertainty region in timeΔtmax is equal to the code epoch length. The length of the fre-quency uncertainty region Δ fmax may vary according to theinitial information: if assisted-GPS data are available, Δ fmax

can be as small as couple of Hertzs or couple of tens of Hertzs.If no Doppler-frequency information exists (i.e., no assis-tance or autonomous GPS), the frequency range Δ fmax canbe as large as few tens of kHz [13].

The time-frequency bin defines the final time-frequencyerror after the acquisition process and it is characterized byone correlator output: the length of a bin in time direction(or the time-bin step) is denoted by (Δt)bin (expressed inchips) and the length of a bin in frequency direction is de-noted by (Δ f )bin. For example, for GPS case, a typical valuefor the (Δt)bin is 0.5 chips [13]. The search procedure canbe serial (if each bin is searched serially in the uncertaintyspace), hybrid (if several bins are searched together), or fullyparallel (if one decision variable is formed for the whole un-certainty space) [13]. This paper focuses on the serial searchapproach.

One of the main features of Galileo system is the intro-duction of longer codes than those used for most GPS sig-nals. Also, the presence of BOC modulation creates some ad-ditional peaks in the envelope of the correlation function, aswell as additional deep fades within ±1 chip from the mainpeak. For this reason, a time-bin step of 0.5 chips is typicallynot sufficient and smaller steps need to be used [5, 10, 11].On the other hand, decreasing the time-bin step will increasethe mean acquisition time and the complexity of the receiver[9].

In the serial search code acquisition process, one decisionvariable is formed per each time-frequency bin (based on thecorrelation between the received signal and a reference code),and this decision variable is compared with a threshold inorder to decide whether the signal is present or absent. Theambiguous-BOC (aBOC) processing means that, when form-ing the decision variable, the received signal is directly corre-lated with the reference BOC-modulated PRN sequence (allthe spectrum is used for both the received signal and refer-ence code).

3. BENCHMARK UNAMBIGUOUS ACQUISITION:B&F METHOD

The presence of BOC modulation in Galileo systems posessupplementary constraints on code search strategies, due tothe ambiguities of the CF envelope. Therefore, better strate-gies should be used to insure reasonable performance (acqui-sition time and detection probabilities) as those obtained forshort codes. One of the proposed strategies to deal with theambiguities of BOC-modulated signals is the unambiguousacquisition (known under several names, such as sidebandcorrelation method or BPSK-like technique).

The original unambiguous acquisition technique, pro-posed by Fishman and Betz in [9, 16], and later modifiedin [6, 10], uses a frequency approach, shown in Figure 2. Inwhat follows, we denote this technique via B&F technique,from the initials of the main authors. The block diagrams ofthe B&F method (single-sideband processing) is illustratedin Figure 2, for upper sideband- (USB-) processing [9, 16].The same is valid for the lower sideband- (LSB-) processing.The main lobe of one of the sidebands of the received sig-nal (upper or lower) is selected via filtering and correlatedwith a reference code, with tentative delay τ and reference

Doppler frequency fD. The reference code is obtained in a

Elena Simona Lohan 3

Upper sideband processing

Lower sideband processing

Upper sidebandfilter

Upper sidebandfilter

Received BOC-modulatedsignal

Reference BOC-modulatedPRN code

Coherent and noncoherent integration

Σ

Towardsdetection

stage

∗

0

0.2

0.4

0.6

0.8

1N

orm

aliz

edP

SD

−4 −3 −2 −1 0 1 2 3 4Frequecy (MHz)

SinBOC(1, 1) spectrum

Figure 2: Block diagram of B&F method, single-sideband processing (here, upper sideband).

similar manner with the received signal, hence the autocor-relation function is no longer the CF of a BOC-modulatedsignal, but it will resemble the CF of a BPSK-modulated sig-nal. However, the exact shape of the resulting CF is not iden-tical with the CF of a BPSK-modulated signal, since some in-formation is lost when filtering out the sidelobes adjacent tothe main lobe (this is exemplified in Section 4). This filteringis needed in order to reduce the noise power. When the B&Fdual-sideband method is used, we add together the USB andLSB outputs and form the dual-sideband statistic.

4. FILTER-BANK-BASED (FBB) METHODS

The underlying principle of the proposed FBB methods isillustrated in Figure 3 and the block diagram is shown inFigure 4. The number of filters in the filter bank is denotedby Nfb and it is related to the number of frequency pieces persideband Npieces via: Nfb = 2Npieces if dual sideband (SB) isused, or Nfb = Npieces if single SB is used. In Figure 3, theupper plot shows the spectrum of a SinBOC(1,1)-modulatedsignal, together with several filters (hereNfb = 4) which coverthe useful part of the signal spectrum (the useful part is con-sidered here to be everything between the main spectral lobesof the signal, including these main lobes). Alternatively, wemay select only the upper (or lower) SB of the signal (i.e.,single-SB processing).

The filters may have equal or unequal frequency widths.Two methods may be employed and they have been denotedhere via equal-power FBB (FBBep), where each filter lets thesame signal’s spectral energy to be passed, thus they have un-equal frequency widths (see upper plot of Figure 3), or equal-frequency-width FBB (FBBefw), where all the filters in the fil-ter bank have the same bandwidth (but the signal power isdifferent from one band to another). An observation oughtto be made here with respect to these denominations: indeed,before the correlation takes place and after filtering the in-coming signal (via the filter bank), the noise power densityis exactly in reverse situation compared to the signal power,

since the noise power depends on the filter bandwidth (i.e.,the noise power is constant from one band to another forthe FBBefw case, and it is variable for the FBBep case). How-ever, the incoming (filtered) signal is correlated with the ref-erence BOC-modulated code. Thus, the noise, which maybe assumed white before the correlation, becomes colourednoise after the correlation with BOC signal, and its spectrum(after the correlation) takes the shape of the BOC powerspectral density. Therefore, after the correlation stage at thereceiver (e.g., immediately before the coherent integrationblock), both signal power density and noise power densityare shaped by the BOC spectrum. Thus, the denominationsused here (FBBep and FBBefw) are suited for both signal andnoise parts, as long as the focus is on the processing after thecorrelation stage (as it is the case in the acquisition).

As seen in Figure 4, the same filter bank is applied toboth the signal and the reference BOC-modulated pseudo-random code. Then, filtered pieces of the signal are corre-lated with filtered pieces of the code (as shown in Figure 4)and an example of the resultant CF is plotted in the lowerpart of Figure 3. For reference purpose, also aBOC and B&Fcases are shown. It is noticed that, when Npieces = 1, the pro-posed FBB methods (both FBBep and FBBefw) become identi-cal with B&F method, and the higher the Npieces is, the widerthe main lobe of the CF envelope becomes, at the expense ofa higher decrease in the signal power.

The block diagram in Figure 4 applies not only to FBBmethods, but also to other GPS/Galileo acquisition meth-ods, such as single/dual SB, and ambiguous-/unambiguous-BOC acquisition methods (i.e., aBOC corresponds to thecase when no filtering stage is applied to the received andreference signals, while B&F corresponds to the case whenNpieces = 1). The complex outputs yi(·), i = 1, . . . ,Nfb of thecoherent integration block of Figure 4 can be written as

yi(

τ, fD,n) = 1

Tcoh

∫ nT+Tcoh

nTri(t)ci(t − τ)e j2π

fDtdt, (1)


−3 −2 −1 0 1 2 3

Frequency (MHz)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Spec

tru

m

Dual sideband processing, equal-power pieces

BOC PSDFilter 1Filter 2

Filter 3

Filter 4

(a)

−3 −2 −1 0 1 2 3

Delay error (chips)

0

0.5

1

1.5

2

2.5

3

3.5

|CF|

2

Squared CF envelope, Npieces = 2, NBOC = 2

BOCB&F, dual SB

FBBep, dual SBFBBefw, dual SB

(b)

Figure 3: Illustration of the FBB acquisition methods, SinBOC(1,1)case. Upper plot: division into frequency pieces, via Nfb = 4 filters(FBBep method). Lower plot: squared CF shapes for 2 FBB meth-ods, compared with ambiguous BOC (aBOC) and unambiguousBetz&Fishman (B&F) methods.

where n is the symbol (or code epoch) index, T is the symbolinterval, ri(t) is the filtered signal via the ith filter, ci(t) is thefiltered reference code (note that the code c(t) before the filterbank is the BOC-modulated spread spectrum sequence), τ

and fD are the receiver candidates for the delay and Dopplershift, respectively, and Tcoh is the coherent integration length(if the code epoch length is 1 millisecond, then the number ofcoherent code epochsNc may be used instead: Tcoh = Nc ms).Without loss of generality, we may assume that a pilot chan-

nel is available (such as it is the case of Galileo L1 band), thusthe received signal r(t) (before filtering) has the form

r(t) =√

Ebc(t − τ)e− j2π fDt + ηwb(t), (2)

where τ and fD are the delay and Doppler shift introducedby the channel, ηwb(t) is the additive white Gaussian noise atwideband level, and Eb is the bit energy.

The coherent integration outputs yi(·) are Gaussian pro-cesses (since a filtered Gaussian processes is still a Gaussianprocesses). Their mean is either 0 (if we are in an incorrecttime-frequency bin) or it is proportional to a time-Doppler

deterioration factor√

EbF (Δτ,Δ fD) [11], with a proportion-ality constant dependent on the number of filters and of theacquisition algorithm, as it will be shown in Section 5. Here,F (·) is the amplitude deterioration in the correct bin due

to a residual time error Δτ and a residual Doppler error Δ fD[11]

F(

Δτ,Δ fD) =

∣

∣

∣

∣R(

Δτ) sin

(

πΔ fDTcoh)

πΔ fDTcoh

∣

∣

∣

∣. (3)

As mentioned above, Δτ = τ− τ, Δ fD = fD− fD, and R(Δτ)is the CF value at delay errorΔτ (CF is dependent on the usedalgorithm, as shown in the lower plot of Figure 3). Moreover,if we normalize the yi(·) variables with respect to their max-imum power, the variance of yi(·) variables (in both the cor-rect and incorrect bins) is proportional to the postintegrationnoise variance

σ2 � 10−(CNR+10log10Tcoh)/10, (4)

where CNR = EbBW/N0 is the Carrier-to-Noise Ratio, ex-pressed in dB-Hz [5, 7, 11], BW is the signal bandwidth afterdespreading (e.g., BW = 1 kHz for GPS and Galileo signals),and N0 is the double-sided noise spectral power density inthe narrowband domain (after despreading or correlation on1 millisecond in GPS/Galileo). The proportionality constantsare presented in Section 5. The decision statistic Z of Figure 4is the output of noncoherent combining of NncNfb complexGaussian variables, where Nnc is the noncoherent integrationtime (expressed in blocks of Nc ms):

Z = 1Nnc

1Nfb

Nnc∑

n=1

Nfb∑

i=1

∣

∣yi(

τ, fD,n)∣

∣

2. (5)

We remark that the coloured noise impact on Z statistic issimilar with the impact of a white noise; the only differencewill be in the moments of Z, as discussed in Section 5.1 (sincea filtered Gaussian variable is still a Gaussian variable, butwith different mean and variance, according to the used fil-ter). Thus, if those Gaussian variables have equal variances,Z is a chi-square distributed variable [17, 18], whose num-ber of degrees of freedom depends on the method and thenumber of filters used. Next section presents the parametersof the distribution of Z for each of the analyzed methods.


c(t)

Ref code

r(t)

Rx sign.

Nfb filters

FB

Nfb filters

FB

Optional stage

... cNfb (t)

c1(t)

... rNfb (t)

r1(t)

∗

∗yNfb

y1

Coherentintegr.

Coherentintegr. ...

||2

||2 ...Nnc∑

Nnc∑

...Nfb∑

Z

Figure 4: Block diagram of a generic acquisition block.

5. THEORETICAL MODEL FOR FBBACQUISITION METHODS

5.1. Test statistic distribution

As explained above, the test statistic Z for aBOC, B&F, andproposed FBBep approaches1 is either a central or a noncen-tral χ2-distributed variable with Ndeg degrees of freedom, ac-cording to whether we have an incorrect (bin � H0) or acorrect (bin � H1) time-frequency bin, respectively. Its non-centrality parameter λZ and its variance σ2

Z are thus given by

λZ = ξλbin

∣

∣F(

Δτ,Δ fD)∣

∣,

σ2Z = ξσ2

bin

σ2

Nnc,

(6)

where F (·) is given in (3), σ2 is given in (4), and ξσ2bin

andξλbin

are two algorithm-dependent factors shown in Table 1(they also depend on whether we are in a correct bin or in anincorrect bin). We remark that the noncentrality parameterused here is the square-root of the noncentrality parameterdefined in [17], such that it corresponds to amplitude lev-els (and not to power levels). The relationship between thedistribution functions and their noncentrality parameter andvariance will be given in (8).

All the parameters in Table 1 have been derived by in-tuitive reasoning (explained below), followed by a thoroughverification of the theoretical formulas via simulations. Forclarity reasons, we assumed that the bit energy is normalizedto Eb = 1 and all the signal and noise statistics are presentwith respect to this normalization.

Clearly, for aBOC algorithm, ξσ2bin= 1 and the noncen-

trality factor ξλbinis either 1 (in a correct bin) or 0 (in an in-

correct bin) [5, 7, 19]. Also, Ndeg = 2Nnc for aBOC, becausewe add together the absolute-squared valued of Nnc complexvariables (or the squares 2Nnc real variables, coming fromreal and imaginary parts of the correlator outputs). For B&F,the noncentrality deterioration factor and the variance dete-rioration factor depend on the normalized power per mainlobe (positive or negative) Pml of the BOC power spectral

1 The case of FBBefw is discussed separately, later in this section.

density (PSD) function. Pml can be easy computed analyti-cally, using, for example, the formulas for PSD given in [3, 4]and some illustrative examples are shown in Figure 5; thenormalization is done with respect to the total signal power,thus Pml < 0.5.; Pml factor is normalized with respect to thetotal signal power, thus Pml < 0.5 (e.g., Pml = 0.428 for Sin-BOC(1,1)). The decrease in the signal and noise power afterthe correlation in B&F method (and thus, the decrease in ξλH1

and ξσ2bin

parameters) is due to the fact that both the signaland the reference code are filtered and the filter bandwidth isadjusted to the width of the PSD main lobe. Also, in dual-SB approaches, the signal power is twice the signal powerfor single SB, therefore, the noncentrality parameter (whichis a measure of the amplitude, not of the signal power) in-creases by

√2. Furthermore, in dual-SB approaches, we add

a double number of noncoherent variables, thus the num-ber of degrees of freedom is doubled compared to single-SBapproaches.

The derivation of χ2 parameters for FBBep is also straight-forward by keeping in mind that the variance of the vari-ables yi is constant for each frequency piece (the filters weredesigned in such a way to let equal power to be passedthrough them). Thus, the noise power decrease factor isξσ2

bin= Pml/Npieces, bin = H0, H1, and the signal power de-

creases to Npieces(P2ml/N

2pieces), thus xλbin = Pml/

√

Npieces for

single SB (and xλbin =√

2Pml/√

Npieces for dual SB).For FBBefw, the reasoning is not so straightforward (be-

cause the sum of squares of Gaussian variables of differentvariances is no longer χ2 distributed) and the bounds givenin Table 1 were obtained via simulations. It was noticed (viasimulations) that the noise variance in the correct and in-correct bins is no longer the same. It was also noticed thatthe distribution of FBBefw test statistic is bounded by two χ2

distributions. Moreover, Pmaxpp is the maximum power perpiece (in the positive or in the negative frequency band). Forexample, if Npieces = 2 and FBBefw approach is used for Sin-BOC(1,1) case, the powers per piece of the positive-sidebandlobe are 0.10 and 0.34, respectively (hence, Pmaxpp = 0.34).Again, these powers can be derived straightforwardly, via theformulas shown in [1, 3, 4, 20].

Figure 6 compares the simulation-based complementaryCDF (i.e., 1-CDF) with theoretical complementary CDFsfor FBBep case (similar plots were obtained for aBOC,B&F, and FBBefw but they are not included here due to


Table 1: χ2 parameters for the distribution of the decision variable Z, various acquisition methods.

Correct bin (hypothesis H1) Incorrect bin (hypothesis H0)

ξλH1ξσ2

H1Ndeg ξλH0

ξσ2H0

Ndeg

aBOC 1 1 2Nnc 0 1 2Nnc

Single-sidebandB& F

Pml Pml 2Nnc 0 Pml 2Nnc

Dual-sidebandB&F

√2Pml Pml 4Nnc 0 Pml 4Nnc

Single-sidebandFBBep and lowerbound of single-sideband FBBefw

Pml√

Npieces

Pml

Npieces2NncNpieces 0

Pml

Npieces2NncNpieces

Dual-sidebandFBBep and lowerbound of dual-sideband FBBefw

√2

Pml√

Npieces

Pml


Pml

Npieces4NncNpieces

Upper bound ofsingle-sidebandFBBefw

Pml√

Npieces

Pmaxpp


Pml

Npieces2NncNpieces

Upper bound ofdual-sidebandFBBefw

√2

Pml√

Npieces

Pmaxpp


Pml

Npieces4NncNpieces

lack of space). For the simulations shown in Figure 6,SinBOC(1,1) signal was used, with coherent integrationlength Nc = 20 milliseconds, noncoherent integration lengthNnc = 2, CNR = 24 dB-Hz, number of samples per BOCinterval Ns = 4, and single-SB filter bank with 4 fil-ters (i.e., Nfb = Npieces = 4). It was also noticed thatthe bounds for FBBefw approach are rather loose. How-ever, simulation results showed that the average behaviorof FBBefw, while keeping between the bounds, is also verysimilar with the average behavior of FBBep [12], therefore,from now on, it is possible to rely on FBBep curves alonein order to illustrate the average performance of proposedFBB methods. We remark that the plots of complementaryCDF were chosen instead of CDF, in order to show bet-ter the tail matching of the theoretical and simulation-baseddistributions.

5.2. Detection probability andmean acquisition times

In serial search acquisition, the detection probability perbin Pdbin (Δτ) is the probability that the decision variable Zis higher than the decision threshold γ, provided that weare in a correct bin (hypothesis H1). Similarly, the falsealarm probability Pfa is the probability that the decision vari-able is higher than γ, provided that we are in an incor-rect bin (hypothesis H0). These probabilities can be easilycomputed based on the cumulative distribution functions(CDFs) of Z in the correct Fnc(·) and incorrect bins Fc(·)[11]:

Pdbin

(

Δτ,Δ fD) = 1− Fnc(γ, λZ),

Pfa = 1− Fc(γ),(7)

2 3 4 5 6 7 8 9 10 11 12

BOC modulation order NBOC

0.36

0.37

0.38

0.39

0.4

0.41

0.42

0.43

Pow

erp

erm

ain

(pos

itiv

eor

neg

ativ

e)lo

beP

ml

Power per main lobe of BOC-modulated signal

Sine BOCCosine BOC

Figure 5: Normalized power per main lobe Pml for BOC-modulatedsignals for various NBOC orders.

where Fnc(·) is the CDF of a noncentral χ2 variable andFc(·) is the CDF of a central χ2 variable, given by [17]:

Fc(z) = 1−Ndeg/2−1∑

k=0

e−z/σ2Z

(

z

σ2Z

)k 1k!

in incorrect bins H0

Fnc(

z, λZ) = 1−QNdeg/2

(

λZ√

2σZ

,

√2zσZ

)

in correct bins H1

(8)


0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

Test statistic levels

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1-C

DF

Matching to χ2 complementary CDF for SSB, FBB

Sim, non-centralTh, non-central

Sim, centralTh, central

Figure 6: Matching with χ2 distributions, (complementary CDF:1-CDF), theory (th) versus simulations (sim), FBBep, Nfb =Npieces = 4.

with σ2Z , Ndeg, and λZ given in (6) and in Table 1, and

QNdeg/2(·) being the generalized Marcum-Q function [17].Due to the fact that the time-bin step may be smaller thanthe 2-chip interval of the CF main lobe, we might haveseveral correct bins. The number of correct bins is: Nt =�2Tc/(Δt)bin�, where Tc is the chip interval. Thus, the globaldetection probability Pd is the sum of probabilities of detect-ing the signal in the ith bin, provided that all the previoustested hypotheses for the prior correct bins gave a misdetec-tion [11]:

Pd(

Δτ0) =

Nt−1∑

k=0

Pdbin

(

Δτ0 + k(Δt)bin,Δ fD)

k−1∏

i=0

(

1− Pdbin

(

Δτ0 + i(Δt)bin,Δ fD))

.

(9)

In (9),Δτ0 is the delay error associated with the first sam-pling point in the two-chip interval, where we have Nt cor-rect bins. Equation (9) is valid only for fixed sampling points.However, due to the random nature of the channels, the sam-pling point (with respect to the channel delay) is randomlyfluctuating, hence, the global Pd is computed as the expecta-tion E(·) over all possible initial delay errors (under uniformdistribution, we simply take the temporal mean):

Pd = EΔτ0

(

Pd(

Δτ0))

, (10)

and the worst detection probability is obtained for the worstsequence of sampling points: Pd,worst = minΔτ0 (Pd(Δτ0)).

The mean acquisition time Tacq for the serial search iscomputed according to the global Pd, the false alarm Pfa, thepenalty time Kpenalty (i.e., the time lost to restart the acqui-

sition process if a false alarm state is reached), and the totalnumber of bins in the search space [21]:

Tacq =2 +

(

2− Pd)

(q − 1)(

1 + KpenaltyPfa)

2Pdτd, (11)

where τd = NncTcoh is the dwell time, q is the total num-ber of bins in the search space, and Pd and Pfa are given by(7) to (10). An example of the theoretical average detectionprobability Pd compared with the simulation results is shownin Figure 7, where a very good match is observed. The smallmismatch at high (Δt)bin for the dual B&F method can be ex-plained by the number of points used in the statistics: about5000 random points have been used to build such statistics,which seemed enough for most of (Δt)bin ranges. However, atvery low detection probabilities, this number is still too smallfor a perfect match. However, the gap is not significant, andlow Pd regions are not the most interesting from the analysispoint of view.

An example of performance (in terms of average andworst detection probabilities) of the proposed FBB methodsis given in Figure 8. The gap between proposed FBB methodsand aBOC method is even higher from the point of view ofthe worst Pd. Here, SinBOC(1,1)-modulated signal was used,and Nc = 20 ms, Nnc = 2. The other parameters are specifiedin the figures captions. The small edge in aBOC average per-formance at around 0.7 chips is explained by the fact that atime-bin step equal to the width of the main lobe of CF en-velope (i.e., about 0.7 chips) would give worse performancethan a slightly higher or smaller steps, due to ambiguities inthe CF envelope. Also, the relatively constant slope in the re-gion of 0.7–1 chips can be explained by the combination ofhigh time-bin steps and the presence of the deep fades in theCF: since the spacing between those deep fades is around 0.7chips for SinBOC(1,1), then a time-bin step of 0.7 chips is theworst possible choice in the interval up to 1 chip. However,there is no significant difference in average Pd for time-binsteps between 0.7 and 1 chip, since two counter-effects aresuperposed (and they seem to cancel each other in the regionof 0.7 till 1 chip from the point of view of average Pd): onone hand, increasing the time-bin step is deteriorating theperformance; on the other hand, avoiding (as much as possi-ble) the deep fades of CF is beneficial. This fact is even morevisible from the lower plot of Figure 8, where worst-case Pdare shown. Clearly, having a time-bin step of about 0.7 chipswould mean that, in the worst case, we are always in a deepfade and lose completely the peak of the main lobe. This ex-plains the minimum Pd achieved at such a step. Also, for stepshigher than 1.5 chips, there is always a sampling sequencethat will miss completely the main lobe of the envelope of CF(thus, the worst Pd will be zero).

It is noticed that FBB methods can work with time-binsteps higher than 1 chip, due to the increase in the main lobeof the CF envelope. Moreover, the proposed FBB methods(both single and dual SB) outperform the B&F and aBOCmethod if the step (Δt)bin is sufficiently high. Indeed, thehigher the time-bin step, the higher is the improvement ofFBB methods over aBOC and B&F methods. We remark thateven at (Δt)bin = 1 chip, we have a significantly high Pd,


0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

(Δt)bin (chips)

10−3

10−2

10−1

100

Pd

Pd at Pfa = 0.001, dual B&F, CNR = 27 dB-Hz

Sim, averageTh, average

Sim, worstTh, worst

(a)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

(Δt)bin (chips)

10−2

10−1

100

Pd

Pd at Pfa = 0.001, dual FBBep, CNR = 27 dB-Hz, Npieces = 2

Sim, averageTh, average

Sim, worstTh, worst

(b)

Figure 7: Comparison between theory and simulations for Sin-BOC(1,1). Left: dual-sideband B&F method. Right: Dual-sidebandFBBep method, Npieces = 2. Nc = 10 milliseconds, Nnc = 5, CNR =27 dB-Hz, Ns = 5.

due to the widening of the CF main lobe. The constant Pdat higher time-bin steps is explained by the fact that, if thestep increases with respect to the correlation function width,only noise is captured in the acquisition block. Thus, increas-ing the step above a certain threshold would not change theserial detection probability, since the decision variable willonly contains noise samples.

On the other hand, by increasing the time-bin step inthe acquisition process, we may decrease substantially themean acquisition time, because the number of bins in the

0 0.5 1 1.5 2 2.5 3


0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Pd

Average Pd , Npieces = 2, CNR = 30 dB-Hz

aBOCSingle B&FDual B&F

Single FBBDual FBB

(a)

0 0.5 1 1.5 2 2.5 3


0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

PdPd,worst, Npieces = 2, CNR = 30 dB-Hz

aBOCSingle B&FDual B&F

Single FBBDual FBB

(b)

Figure 8: Average (upper) and worst (lower) detection probabili-ties versus (Δt)bin ambiguous and unambiguous BOC acquisitionmethods (FBBep was used here).

search space (see (11) is directly proportional to (Δt)bin. Forexample, if the code epoch length is 1023 chips and onlyone frequency bin is searched (assisted acquisition), q =�1023/(Δt)bin�. Moreover, the computational load requiredfor implementing a correlator acquisition receiver per unit oftime uncertainty is inversely proportional to (Δt)2

bin [9], thus,when (Δt)bin increases, the computational load decreases.

An example regarding the needed time-bin step in or-der to achieve a certain detection probability, at fixed CNRand false alarm probability, is shown in what follows. We


25 26 27 28 29 30 31

CNR (dB-Hz)

0

0.5

1

1.5

2(Δt)

bin

(ch

ips)

Step needed to achieve a target Pd = 0.9, (average case)

Dual SB, FBBep

Dual SB, B&F

(a)

25 26 27 28 29 30 31

CNR (dB-Hz)

0

0.5

1

1.5

(Δt)

bin

(ch

ips)

Step needed to achieve a target Pd = 0.9, (average case)

Single SB, FBBep

Single SB, B&F

(b)

25 26 27 28 29 30 31

CNR (dB-Hz)

101

102

103

MA

T

Achieved MAT [s] at considered step

Dual SB, FBBDual SB, B&F

(c)

25 26 27 28 29 30 31

CNR (dB-Hz)

101

102

103

104

MA

T


Single SB, FBBep

Single SB, B&F

(d)

Figure 9: Step needed to achieve a target average Pd = 0.9, at false alarm Pfa = 10−3 and corresponding mean acquisition time, SinBOC(1,1)signal. Code length 4092 chips, penalty factor Kpenalty = 1, single frequency-bin. Npieces = 2 for FBBep. Left: dual sideband. Right: singlesideband.

assume a SinBOC(1,1)-modulated signal, a CNR = 30 dB-Hz, and a target average detection probability of Pd = 0.9 atPfa = 10−3. For these values, we need a step of (Δt)bin = 1.2chips for the dual-sideband B&F method (which will cor-respond to a mean acquisition time Tacq = 86.24 s for sin-gle frequency serial search and 4092-chip length code) and astep of (Δt)bin = 1.7 chips for dual-sideband FBBep methodwith Npieces = 2 (i.e., Tacq = 58.14 s). Thus, the step can beabout 50% higher for dual-sideband FBB case than for dual-sideband B&F case, and we may gain about 48% in the MAT(i.e., MAT is 48% less in dual-SB FBB case than in dual-SBB&F case). For single-sideband approaches, the differencesbetween FBB and B&F methods are smaller. An illustrativeplots is shown in Figure 9, where the needed steps and theachievable mean acquisition times are given with respect toCNR. We notice that FBB methods outperform B&F meth-ods at high CNRs. Below a certain CNR limit (which, ofcourse, depends on the (Nc, Nnc) pair), B&F method maybe better than FBB method.

The optimal number of pieces or filters to be used in thefilter bank depends on the CNR, on the method (single ordual SB), and on the BOC modulation orders. From simu-lation results (not included here due to lack of space), bestvalues between 2 and 6 have been observed. This is due tothe fact that a too high Npieces parameter would deterioratethe signal power too much.

We remark that the choice of the penalty factor has notbeen documented well in the literature. The penalty time se-

lection is in general related to the quality of the followingcode tracking circuit. There is a wide range of values thatKpenalty may take and no general rule about the choice ofKpenalty has been given so far, to the author’s knowledge. Forexample, in [22] a penalty factor Kpenalty = 1 was consid-ered; in [23] simulations were carried out for Kpenalty = 2, in[24] a penalty factor of Kpenalty = 103 was used, while in [25]we have Kpenalty = 106. Penalty factors with respect to dwelltimes were also used in the literature, for example: Kpenalty =105/(NcNnc) [26, 27], or Kpenalty = 107/(NcNnc) [27] (in oursimulations, NcNnc = 40 ms). Therefore, Kpenalty may spreadover an interval of [1, 106], therefore, in our simulations weconsidered the 2 extreme cases: Kpenalty = 1 (Figure 9) andKpenalty = 106 (Figure 10). Figure 10 uses exactly the sameparameters as Figure 9, with the exception of the penaltyfactor, which is now Kpenalty = 106. For Kpenalty = 106 ofFigure 10, MAT for the dual-sideband B&F method becomesTacq = 8.62 ∗ 104, which is still higher than MAT for thedual-sideband FBBep (Tacq = 5.8 ∗ 104 s). Similar improve-ments in MAT times via FBB processing (as for Kpenalty = 1)are observed if we increase the penalty time.

The plots with respect to the receiver operating charac-teristics (ROC) are shown in Figure 11 for a CNR of 30 dB-Hz. ROC curves are obtained by plotting the misdetectionprobability 1−Pd versus false alarm probability Pfa [28]. Thelower the area below the ROC curves is, the better the per-formance of the algorithm is. As seen in Figure 11, the dualsideband unambiguous methods have the best performance.


25 26 27 28 29 30 31

CNR (dB-Hz)

104

105

106

MA

T


Dual SB, FBBep

Dual SB, B&F

(a)

25 26 27 28 29 30 31

CNR (dB-Hz)

104

105

106

107

MA

T


Single SB, FBBep

Single SB, B&F

(b)

Figure 10: Mean acquisition time corresponding to the step needed to achieve a target average Pd = 0.9, at false alarm Pfa = 10−3, Sin-BOC(1,1) signal. Code length 4092 chips, penalty factor Kpenalty = 106, single frequency-bin. Npieces = 2 for FBBep. Left: dual sideband. Right:single sideband.

10−10 10−8 10−6 10−4 10−2

False alarm probability Pfa

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Mis

-det

ecti

onpr

obab

ility

1-Pd

ROC, (Δt)bin = 0.5 chips, CNR = 30 dB-Hz

aBOCSingle BFDual BF

Single FBBDual FBB

(a)

10−10 10−8 10−6 10−4 10−2

False alarm probability Pfa

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Mis

-det

ecti

onpr

obab

ility

1-Pd

ROC, (Δt)bin = 1.5 chips, CNR = 30 dB-Hz

aBOCSingle BFDual BF

Single FBBDual FBB

(b)

Figure 11: Receiver operating characteristic for CNR = 30 dB-Hz, SinBOC(1,1) signal, Nc = 20, Nnc = 2. Left: (Δt)bin = 0.5 chips; right(Δt)bin = 1.5 chips.

At low time-bin steps (e.g., (Δt)bin = 0.5 chips), the FBB andB&F methods behave similarly, as it has been seen before alsoin Figure 8. The main advantage of FBB methods is observedfor time-bin steps higher than one chip, as shown in the leftplot of Figure 11. For both time-bin steps considered here,the single sideband unambiguous methods have a thresholdfalse alarm, below which their performance becomes worsethan that of ambiguous BOC approach. This threshold de-

pends on the CNR, on the integration times, and on the time-bin step and it is typically quite low (below 10−5).

6. CONCLUSIONS

This paper introduces a new class of code acquisition meth-ods for BOC-modulated CDMA signals, based on filter bankprocessing. The detailed theoretical characterization of this


new method has been given and theoretical curves were val-idated via simulations. The performance comparison withother methods (i.e., ambiguous BOC and Betz&Fishmansideband correlator) showed that FBB techniques can be suc-cessfully employed if the target is to increase the time-binstep of the acquisition process and to minimize the mean ac-quisition times and the computational load of the correlator.

ACKNOWLEDGMENTS

This work was carried out in the project “Advanced Tech-niques for Personal Navigation (ATENA)” funded by theFinnish Funding Agency for Technology and Innovation(Tekes). This work has also been supported by the Academyof Finland.

REFERENCES

[1] J. W. Betz, “The offset carrier modulation for GPS moderniza-tion,” in Proceedings of the International Technical Meeting ofthe Institute of Navigation (ION-NTM ’99), pp. 639–648, SanDiego, Calif, USA, January 1999.

[2] A. Burian, E. S. Lohan, and M. Renfors, “BPSK-like methodsfor hybrid-search acquisition of Galileo signals,” in Proceedingsof the IEEE International Conference on Communications (ICC’06), vol. 11, pp. 5211–5216, Istanbul, Turkey, June 2006.

[3] E. S. Lohan, A. Lakhzouri, and M. Renfors, “Binary-offset-carrier modulation techniques with applications in satel-lite navigation systems,” Wireless Communications and MobileComputing, vol. 7, no. 6, pp. 767–779, 2006.

[4] E. S. Lohan, A. Lakhzouri, and M. Renfors, “Spectral shap-ing of Galileo signals in the presence of frequency offsets andmultipath channels,” in Proceedings of 14th IST Mobile & Wire-less Communications Summit, Dresden, Germany, June 2005,CDROM.

[5] S. Fischer, A. Guerin, and S. Berberich, “Acquisition conceptsfor Galileo BOC(2,2) signals in consideration of hardware lim-itations,” in Proceedings of the 59th IEEE Vehicular TechnologyConference (VTC ’04), vol. 5, pp. 2852–2856, Milan, Italy, May2004.

[6] N. Martin, V. Leblond, G. Guillotel, and V. Heiries, “BOC(x,y)signal acquisition techniques and performances,” in Proceed-ings of the 16th International Technical Meeting of the SatelliteDivision of the Institute of Navigation (ION GPS/GNSS ’03),pp. 188–198, Portland, Ore, USA, September 2003.

[7] B. Bandemer, H. Denks, A. Hornbostel, A. Konovaltsev, andP. R. Coutinho, “Performance of acquisition methods forGalileo SW receivers,” in Proceedings of the European Navi-gation Conference (ENC-GNSS ’05), Munich, Germany, July2005, CDROM.

[8] B. C. Barker, J. W. Betz, J. E. Clark, et al., “Overview of theGPS M code signal,” in Proceedings of the International Tech-nical Meeting of the Institute of Navigation (ION-NTM ’00),Anaheim, Calif, USA, January 2000, CDROM.

[9] P. Fishman and J. W. Betz, “Predicting performance of directacquisition for the M-code signal,” in Proceedings of the Inter-national Technical Meeting of the Institute of Navigation (ION-NTM ’00), pp. 574–582, Anaheim, Calif, USA, January 2000.

[10] V. Heiries, D. Roviras, L. Ries, and V. Calmettes, “Analysis ofnon ambiguous BOC signal acquisition performance,” in Pro-ceedings of the 18th International Technical Meeting of the Satel-lite Division of the Institute of Navigation (ION-GNSS ’05),Long Beach, Calif, USA, September 2005, CDROM.

[11] E. S. Lohan, “Statistical analysis of BPSK-like techniques forthe acquisition of Galileo signals,” in Proceedings of the 23rdAIAA International Communication Systems Conference (IC-SSC ’05), Rome, Italy, September 2005, CDROM.

[12] E. S. Lohan, “Filter-bank based technique for fast acquisitionof Galileo and GPS signals,” in Proceedings of the 17th IEEEInternational Symposium on Personal, Indoor and Mobile Ra-dio Communications (PIMRC ’06), pp. 1–5, Helsinki, Finland,September 2006.

[13] E. D. Kaplan, Understanding GPS: Principles and Applications,Artech House, London, UK, 1996.

[14] P. W. Ward, “GPS receiver search techniques,” in Proceedingsof the IEEE Position Location and Navigation Symposium, pp.604–611, Atlanta, Ga, USA, April 1996.

[15] M. Katz, Code acquisition in advanced CDMA networks, Ph.D.thesis, University of Oulu, Oulu, Finland, 2002.

[16] J. Betz and P. Capozza, “System for direct acquisition of re-ceived signals,” US patent no. 2004/0071200 A1, April 2004.

[17] J. Proakis, Digital Communications, McGraw-Hill, New York,NY, USA, 4th edition, 2001.

[18] R. R. Rick and L. B. Milstein, “Optimal decision strate-gies for acquisition of spread-spectrum signals in frequency-selective fading channels,” IEEE Transactions on Communica-tions, vol. 46, no. 5, pp. 686–694, 1998.

[19] F. Bastide, O. Julien, C. Macabiau, and B. Roturier, “Analysisof L5/E5 acquisition, tracking and data demodulation thresh-olds,” in Proceedings of the International Technical Meeting ofthe Satellite Division of the Institute of Navigation (ION-GPS’02), pp. 2196–2207, Portland, Ore, USA, September 2002.

[20] S. H. Raghavan and J. K. Holmes, “Modeling and simulation ofmixed modulation formats for improved CDMA bandwidthefficiency,” in Proceedings of the 60th IEEE Vehicular Technol-ogy Conference (VTC ’04), vol. 6, pp. 4290–4295, Los Angeles,Calif, USA, September 2004.

[21] J. Holmes and C. Chen, “Acquisition time performance of PNspread-spectrum systems,” IEEE Transactions on Communica-tions, vol. 25, no. 8, pp. 778–784, 1977.

[22] G. J. R. Povey, “Spread spectrum PN code acquisition usinghybrid correlator architectures,” Wireless Personal Communi-cations, vol. 8, no. 2, pp. 151–164, 1998.

[23] W. Zhuang, “Noncoherent hybrid parallel PN code acquisitionfor CDMA mobile communications,” IEEE Transactions on Ve-hicular Technology, vol. 45, no. 4, pp. 643–656, 1996.

[24] E. A. Homier and R. A. Scholtz, “Hybrid fixed-dwell-timesearch techniques for rapid acquisition of ultra-wideband sig-nals,” in Proceedings of the International Workshop on Ultra-Wideband Systems, Oulu, Finland, June 2003.

[25] B.-J. Kang and I.-K. Lee, “A performance comparison of codeacquisition techniques in DS-CDMA system,” Wireless Per-sonal Communications, vol. 25, no. 2, pp. 163–176, 2003.

[26] O.-S. Shin and K. B. Lee, “Utilization of multipaths for spread-spectrum code acquisition in frequency-selective Rayleigh fad-ing channels,” IEEE Transactions on Communications, vol. 49,no. 4, pp. 734–743, 2001.

[27] D. DiCarlo and C. Weber, “Multiple dwell serial search: perfor-mance and application to direct sequence code acquisition,”IEEE Transactions on Communications, vol. 31, no. 5, pp. 650–659, 1983.

[28] S. Soliman, S. Glazko, and P. Agashe, “GPS receiver sensitiv-ity enhancement in wireless applications,” in Proceedings ofthe IEEE MTT-S International Tipical Symposium on Technolo-gies for Wireless Applications, pp. 181–186, Vancouver, Canada,February 1999.

satellite communication

Documents

article id

institute of communications

packetsatellite communications

anton donner

satellite channels

generation satellite

satellite mimochannel

dvbs2 systems